Even if i did miss by a few inches ( GOD FORBID) and hit the jaw, the shock of a big fast bullet out of a 300 mag will knock a deer out cold , and he would bleed to death before he came too.
Wow. I had missed that the first time.
I've helped look for deer that other hunters have shot in the head that flopped over, then came to and ran off with a wound to the cranium. Bleeding to death from a shot-off jaw is NOT very likely. Also, with the hinged jaw, the shock imparted to the CNS is very likely not going to put the animal down.