Second, I would think someone would pass out long and bleed to death before they finished cutting off their own hand.
Aron Ralston managed a similar feat, and he didn't have anything nearby with which to close the wound. Had he not been rescued when he was, Ralston WOULD have bled to death, and then we wouldn't have the movie 127 Hours. Merle at least had the fortune of locating a Bunsen burner.