If the dog is "killing" your dog, pet or livestock (doesn't specify how to prove they were killing and not just attacking) there is a statute that gives you a "good defense" for killing the attacking dog, but it doesn't necessarily make it legal. So if you want to kill the dog, get it to attack you. I imagine most places allow you to shoot a dog that is attacking you. (kidding. mostly.)

https://thefirearmfirm.com/can-i-shoot-a-dog-attacking-my-dog/