It can be done by giving Plot3D the right options.

With[{ϵ = .05}, Plot3D[Sin[x y], {x, 0, 10}, {y, 0 - ϵ, 3 + ϵ}, PlotRangePadding -> 0.6, PlotStyle -> Transparent, BoundaryStyle -> None, Boxed -> False, AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}}, FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}}, FaceGridsStyle -> Directive[Dashed], AxesLabel -> {"X", "Y", "Z"}, MeshFunctions -> {#2 &}, Mesh -> {Range[0, 3]}, MeshStyle -> Directive[Thickness[.009]], Lighting -> "Neutral"]] 

It takes a lot fiddling with the options to get the plot to look your picture.

It can be done by giving Plot3D the right options.

With[{ϵ = .05}, Plot3D[Sin[x y], {x, 0, 10}, {y, 0 - ϵ, 3 + ϵ}, PlotRangePadding -> 0.6, PlotStyle -> Transparent, BoundaryStyle -> None, Boxed -> False, AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}}, FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}}, FaceGridsStyle -> Directive[Dashed], AxesLabel -> {"X", "Y", "Z"}, MeshFunctions -> {#2 &}, Mesh -> {Range[0, 3]}, MeshStyle -> Directive[Thickness[.009]], Lighting -> "Neutral"]] 

It takes a lot fiddling with the options to get the plot to look like your picture. Also, note the it was necessary to extend the plot range of the y-domain.