Difference

Wire the thing you want to keep into Base and the thing to remove into Cutter. This is the only way to open a hole that goes right through, an alcove, or a lip that overhangs. Pushing a surface inward can make a dent or a bowl, but a dented surface is still one surface: it can never break through.

Every cutter is removed at once, so overlapping cutters do not double up. Both sides need to be simple solids, so cut first and reshape afterwards, not the other way round.

Cut with an icosahedron or a box rather than a ball. A ball pinches at its poles into slivers, and that is the one arrangement the cut cannot resolve; it fails at some positions and not others, which is worse than failing everywhere.

Cut before you displace, never after. A surface that has already been pushed around is no longer a simple solid, and the cut will take away material that should have stayed.