I've tried to explain this to my dog. I buy him the best food available, grain free, and he gets oodles of herbal dog treats...Yet he still feels the need to catch, kill and partially devour squirrels, possums and feral kitties. I've seen him spring about six feet in the air to snatch a squirrel right off a tree.
Your dog has a serious need to hunt. I once had a Wiemar who did that, but she was more into birds. She really wouldn’t eat much of them, just caught a lot of them. She would stand for hours sneaking up on a bird, then lunge quite a distance when in range. It was quite a sight to see.
Once she dropped the bird though, she never seemed to go back to it. Other than the puncture marks, she wouldn’t eat much.
The only thing that worked for her was to tie her up, which I just couldn’t do, she just loved to run the acres of our yard.
With our wind dogs we let them tear into the fresh kill so they could draw a scent. But the dogs didn’t run the deer, they just sat in the swamp buggy and nosed the wind for us by barking.