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Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back.

Of course such implementation means that will be deleted only cells, which by default are auto-grouped with input cell: manually grouped cells won't be deleted even if they have style "Output" – that is because manual grouping changes the groping behavior by adding the option CellGroupingRules->{"GroupTogetherGrouping", 10000.}. It seems not reasonable to delete manually grouped cells because among them may preset non-output cells, for example "Input" cells and so on. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.

Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back.

Of course such implementation means that will be deleted only cells, which by default are auto-grouped with input cell: manually grouped cells won't be deleted even if they have style "Output" – that is because manual grouping changes the groping behavior by adding the option CellGroupingRules->{"GroupTogetherGrouping", 10000.}. It seems not reasonable to delete manually grouped cells because among them may present non-output cells, for example "Input" cells and so on. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.

Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back.

Of course such implementation means that will be deleted only cells, which by default are auto-grouped with input cell: manually grouped cells won't be deleted even if they have style "Output" – that is because manual grouping changes the groping behavior by adding the option CellGroupingRules->{"GroupTogetherGrouping", 10000.}. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.

Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back.

Of course such implementation means that will be deleted only cells, which by default are auto-grouped with input cell: manually grouped cells won't be deleted even if they have style "Output" – that is because manual grouping changes the groping behavior by adding the option CellGroupingRules->{"GroupTogetherGrouping", 10000.}. It seems not reasonable to delete manually grouped cells because among them may preset non-output cells, for example "Input" cells and so on. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.

Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back. Of course this means that will be deleted only cells, which by default are grouped with input cell. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.

Currently I have come to a much more complicated solution than I wished, which completely depends on the automatic grouping behavior (which I temporarily switch on):

SetOptions[EvaluationNotebook[], {CellProlog :> AbortProtect[ Module[{nb = EvaluationNotebook[], evalCell = EvaluationCell[], cells, pos, grouping, groupingRules}, If[CurrentValue[NextCell[], CellGroupingRules] == "OutputGrouping", FrontEndExecute@FrontEnd`NotebookSuspendScreenUpdates[nb]; grouping = CurrentValue[nb, CellGrouping]; groupingRules = CurrentValue[evalCell, CellGroupingRules]; CurrentValue[nb, CellGrouping] = Automatic; CurrentValue[evalCell, CellGroupingRules] = "InputGrouping"; SelectionMove[evalCell, All, CellGroup, AutoScroll -> False]; If[Length[cells = SelectedCells[]] > 1, pos = Position[cells, evalCell]; If[pos =!= {} && pos[[1, 1]] < Length[cells], NotebookDelete[cells[[pos[[1, 1]] + 1 ;;]]]] ]; CurrentValue[evalCell, CellGroupingRules] = groupingRules; CurrentValue[nb, CellGrouping] = grouping; FrontEndExecute@FrontEnd`NotebookResumeScreenUpdates[nb];];]]}] 

Note that I set CellGrouping to the default Automatic for the EvaluationNotebook[], and CellGroupingRules to the default "InputGrouping" for EvaluationCell[] in order to have it auto-grouped with next output cells (for the cases when automatic grouping is switched off), then I revert the original values of these options back. 

Of course such implementation means that will be deleted only cells, which by default are auto-grouped with input cell: manually grouped cells won't be deleted even if they have style "Output" – that is because manual grouping changes the groping behavior by adding the option CellGroupingRules->{"GroupTogetherGrouping", 10000.}. This differs from the standard behavior where all pre-existing output will be deleted on the base of the presence of both CellAutoOverwrite -> True and GeneratedCell -> True options.

Still looking for a better way to do it.

P.S. The whole approach has an issue: by the time the contents of the cell starts executing, the output will already be deleted, and therefore, for example, NextCell[] will return a different value than by default.