I'll bet Richard Haw will know more precisely, but I had an old F with a bent aperture lever (caused by lens over-rotating when it lost its limiting screw) and it worked just fine with the bent lever. There's not much room for it to go and I doubt it can completely clear the lens without going very far. Looking inside various cameras I don't see much room to bend it out of the way, which leaves cutting or breaking.
As an alternative to cutting it off, though, I would first take the lens off and see if the lever can still be moved with a finger or with the stop down button. It starts at the top and goes down, in a slot. If you can move it by hand or still use the button, one alternative might be to try jamming it in the down position. A piece of plastic that fits tightly might work, or if you're not worried about ever fixing it, maybe hold the lever down and fill the slot with hot glue. Make sure the plastic doesn't stand high enough to hit the lens's aperture lever.
This cannot work on old mechanical cameras, because the aperture lever is coupled to the mirror, which won't come back down, but I tried holding the lever down on a D3200 and a D7100 and it functioned. Perhaps the same decoupling that keeps stop down metering from working also changes this.
There used to be another temporary solution to this, for lenses that have an aperture ring. If you back off the lens a few degrees, the lever stops functioning and the lens becomes fully manual. That won't work for G lenses, and for any AF lens you have to remount it fully to get electrical contact, but you can use it as a DOF preview on cameras that lack it, and on newer cameras that don't do stop down metering, you can use it to trick the camera into working with a lens that is automatic but not meter coupled (such as pre-AI T4 mounts or old Vivitars that don't adapt well to AI conversion). Of course you have to be careful that the lens does not fall out and land on your toes.
