Typically animals are killed with a low caliber penetrating device administered in the correct location. It's fast and humane. Because It's fast, it keeps the adrenaline level low, (adrenaline is bad for meat flavor). I believe the large cleaver would have been used for butchering purposes. Now days, the killing instrument is probably pneumatic. If you've seen the movie "No Country for Old Men", you know what I mean.
I've heard bison are very hard to kill. Thick skulls I guess. Kind of like some of you guys.
Later
Brent
It is not possible to taste adrenaline in the meat no matter how much is present.
I am not really sure what "humane" means, but if you sever the carotid arteries with a knife, death comes fast (within seconds) and is almost painless. Same effect as if you would manually stop the heart, Mongol style.