A few years ago, I was hunting with my buddy when he shot a doe. I walked over to the area he was hunting and he was getting ready to gut it. I headed back to my stand when he called out to me. It kicked when he started to cut. Not sure why, but he handed the knife to me.....maybe it had freaked him out a bit...I stabbed the blade into the deer's throat and cut outward. Quickly bled out. no fuss. Be careful of the legs though...the hooves could hurt you.
maybe 7 years ago we had a deer get hit in front of our house and break it's back. I used my bow to put an arrow thru the lungs. Again it died quickly. If you don't want to get close to it or you don't want to dispatch it up close and personal, then step back 10 feet so you shoot at an angle and your bullet will not come back your way.