1: Hang the deer by it's head on a sturdy tree limb with heavy rope or whatever. Make sure the limb and rope is strong and the deer is off the ground.
2: Make cuts around the lower legs so the skin will peel off like a sock. Cut the skin around the neck and all the way down the belly (most wil already be cut from dressing it out.
3: Make a small loop in a nylon rope (best because it stretches) by tying a knot in a folded section. Run the rope through the loop so it will tighten when pulled. Use a strong size nylon rope (maybe 1/2 inch)
4: Peel enough skin from the back of the neck to wrap around a golf ball (about 6 inches. Put the ball on the hair side of the skin and wrap the skin around it, flesh outside. Hold the skin tight around the ball and slip the nylon rope over the covered ball. Pull tight so it will not fall off.
5: Tie the rope to your bumper and slowly pull away. The skin will easily peel off and the deer will be clean, no hair or debris. Just be sure to pull in a direction that will not result in the deer swinging back into the tree trunk and getting it dirty. You could wrap a sheet around the tree but I've never had the need. You can quarter the deer while hanging or wrap the skinned deer and take it home for butchering.
This method will not damage the deer or the skin and only takes a couple minutes. If you save the shin you can use a pressure washer to remove the meat and whatever. That also saves a lot of time than using a knife.
We have skinned a lot of deer with this method and never had a problem except when I tied to a weak limb once. Had to clean off leaves and grass with a pressure washer.
Hope this method saves someone time and effort. Ed.