Generally speaking it's a good idea to bleed any hunted animal before gutting. Even if the heart has stopped before you get to it (though for big game you really want to make sure it's dead before you do this) sticking the animal will improve the meat quality, and will make the gutting process a little less of a blood bath.
Deer and elk have an artery along the spine that will pop like a balloon when you gut them if you don't stick them first, and that gets blood all over the tenderloins and hind quarters.
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