the deer is usually killed by wolves by the wolves tearing the guts out of the deer while it is alive.
I don't consider myself an authority, but I've seen enough wildlife documentaries to know a thing or two about how predators hunt and kill, no matter whether they are lions in Africa or wolves in Poland. They usually either go for the throat to cut the artery, brake the prey's neck or put the prey's nose in their mouth in order to suffocate it.
I harvest small deer because they are the best eating
And that's the type of prey wolves are likely to kill quickly:
"With medium-sized prey, such as roe deer or sheep, wolves kill by biting the throat, severing nerve tracks and the carotid artery, thus causing the animal to die within a few seconds to a minute."
en.m.wikipedia.org/wiki/Hunting_behavior_of_gray_wolves
So there goes your theory about "saving" the deer from being eaten alive.
Exactly so we have a hunting season on the wolves too to control the balance.
Are there any limits on how many deer, wolves, etc. hunters can kill in the US?
And in what area were wolves "planted"? In Michigan?:
wolf.org/wolf-recovery-in-michigan/
"At one time, all of what is now Michigan was home to wolves. However, the pattern of habitat destruction, wolf persecution and extirpation by humans which occurred in most of the eastern United States, continued into Michigan with European settlers. A bounty was established
in 1838, at a time when wolves were already nearly eliminated from the southern Lower Peninsula of the state."