If they are still alert dispatching via knife to throat wouldn't be the safest idea. A few years back a hunter here was gored and died by doing this on his wounded buck. I would put another round in them or back away and let nature take its course.

If they are basically down and out but still mustering breaths you could cut the throat but I would probably error on the side of caution and wait it out.

I have seen a few deer play possum so whatever you do use caution. If unsure a poke in the eye with a stick will tell you the score. If they blink be careful of your next move!!!!!

I actually approachgame from the rear this way they have a clear escape route that I am not in the path of. This allows me to see chest wall movementsasI get in tightbut usually if they havemuch left when coming from the rear they will try to re-position to see the pursuer.