Point 1 - If you hit a deer in the vitals (heart lung) it will die. It may take 5-10 seconds. But it will die. How far can a deer run in 10 seconds?

Point 2 - Shoot does in the head with a rifle. Dont tell me its not ethical, been doing it for years with a !00% success ratio. You hit her shes dead. You miss, you get to hunt her again.