I have not had the opportunity with a bow but I have taken one with a slug gun. It was a doe in fine condition missing the lower part of a hind leg.
If I see a wounded or suffering animal I would take it. Hereabouts if it proves unfit for consumption the DEC will issue you a replacement tag.
We have a cat that lost a leg as a tiny kitten (animal attack: coyote/fox/dog?). Someone left him at a shelter so the history was unknown. Being known soft touches the local shelter asked it we would take him (thankfully AFTER all the vet/surgery that a local vet did pro buono).
At the time it looked like it would be just to make him comfortable for a few days until it was over. This was after the dressings came off and he started to come around. He was tore up top, bottom and the leg gone (shoulder and all).
This is whhat he looks like now. Doesn't walk very well, so he runs everywhere.
We have an attached two-car garage and he begs to go out there and hunt. Bless his heart he brings us mice regularly.
Now, granted an indoor cat leads an easier life than a deer, but three legs run almost as well as four from what I have observed. Sure is pitiful to watch him walk and when he junps down off furniture sometimes he bottoms out.