The only time I've put down a deer and it didn't flop around for awhile was when I shot one in the back of the head at a 45 degree angle, mafia execution style. That deer was DRT.
I had a deer once who dragged itself by its front legs (hind legs were barely attached) through a trailer park faster then I could jog after it. Myself and the original 911 caller chased the thing through front yards and over & under fences. It finally ran into some woods but it still would not let me get close enough to it for an accurate pistol shot. I ended up shooting it from 25-30 yards away with the AR. A single 5.56 round, just under the eye, killed it instantly. If I could I'd use the AR for every deer now. But that's not going to happen.