The refs buffer has options to filter to merged branches, however the user interface is a little surprising. From the "References Buffer" section:

‘y’ (‘magit-show-refs’) This command lists branches and tags in a dedicated buffer.

 However if this command is invoked again from this buffer or if it is invoked with a prefix argument, then it acts as a transient prefix command, which binds the following suffix commands and some infix arguments. 

Therefore you can access the show-refs transient by running C-u M-x magit-show-refs, or with  yy in vanilla emacs, or yr yr in Evil mode.

Once you have the transient popup open, you can refine the view with -M setting the value to the merge target  (E.g develop or  main).

Lastly, type y to compare against  HEAD. The refs list you are left with should only contain merged branches.

Highlight all the branches you would like to delete, then press k in vanilla Emacs, or x in Evil (magit-delete-thing) to delete the selection.

Remember, you can set and save default transient values with  C-x  s and C-x C-s respectively.

The refs buffer has options to filter to merged branches. 
Quoting C-hig (magit)References Buffer:

‘y’ (‘magit-show-refs’) 
This command lists branches and tags in a dedicated buffer. However if this command is invoked again from this buffer or if it is invoked with a prefix argument, then it acts as a transient prefix command

Therefore you can access that transient menu with  yy¹

Within the transient menu you can refine the view with - M setting the value to the merge target  (E.g develop or  main).

Then type y to execute the command, comparing against  HEAD. The refs list you are left with should only contain merged branches.

Now highlight all the branches you would like to delete, then press k to delete the selection.²

Remember that you can set and save default transient values with  C-x s and C-xC-s respectively.

¹ or C-uM-x magit-show-refs, or in Evil it's yryr.

² or M-x magit-delete-thing, or in Evil it's x.

The refs buffer has options to filter to merged branches. E.g.:

yy-My

Then just highlight all those branches and type k

The refs buffer has options to filter to merged branches, however the user interface is a little surprising. From the "References Buffer" section:

‘y’ (‘magit-show-refs’) This command lists branches and tags in a dedicated buffer.

 However if this command is invoked again from this buffer or if it is invoked with a prefix argument, then it acts as a transient prefix command, which binds the following suffix commands and some infix arguments. 

Therefore you can access the show-refs transient by running C-u M-x magit-show-refs, or with yy in vanilla emacs, or yr yr in Evil mode.

Once you have the transient popup open, you can refine the view with -M setting the value to the merge target (E.g develop or main).

Lastly, type y to compare against HEAD. The refs list you are left with should only contain merged branches.

Highlight all the branches you would like to delete, then press k in vanilla Emacs, or x in Evil (magit-delete-thing) to delete the selection.

Remember, you can set and save default transient values with C-x s and C-x C-s respectively.