I've own German shepards all my life and I have to say in my opinion a German Shepard can and will kill livestock no matter how well it's trained. My dog bear whom I liove and is so well trained otherwise killed one of my chickens and chased my goats all over the yard when he got lose in the yard. He jumped off the deck and tore up my chick I couldn't get there fast enough to stop him. So yes. They definitely can kill your animals.