Well, this is the consequence of letting it outside unfortunately- on top of risk of injury and death but I’m sure y’all know that already. There’s not really an effective way to train them against this behaviour the way you might a dog.

So long as there’s critters outside the cat is going to hunt them. Maybe you could try to give the kitty a snag safe cat collar with a bell? It might alert the wildlife so they have time to avoid being caught.