I think FULLY dynamic dismembering (that you can cut off 'things' at any position) isn't possible with 3DGS. But I've got two ideas. I don't know
if it works but you can try it:

1: You can use different skins together with the OVERLAY-flag (which makes every black (0,0,0) pixel transparent). 'just' change the
skin to another, where everything which shouldn't be visible is black.

2: The same method - but using a shader and a mask instead of different skins. A bit complicated if you don't know much about shaders, but it would be possible to make any combination of areas invisible with only using 2 skins (it would be also possible with one).