Well, I've never watched them.
They do have a bunch of legs left you know. I have wondered about it, but the ones with no claws keep climbing back in the traps so they must manage OK. The taking of both claws started a few years ago. Stone crabs bring a big bunch of money to south Florida and I doubt the state would let anything happen to the resorce if they could prevent it. They are looking for a good harvest this year being that hurricanes left us alone.
The claws get cliped at the first joint, if you break or tear the claw off you risk killing the crab as they bleed. The claws pop when they come off; it seems to be an escape mechanism, like a lizzard's tail coming off.