Once a dog kills, it is near impossible to stop it. In my opinion, and animal killing dog has no place on a farm with animals. It would either live in an escape proof pen, which I think cruel, or it would be OFF THE FARM.
OP- find the dog a new home. I have a greyhound and have had a few in the past. I also have cats, so I can only adopt the greyhounds that have tested cat-safe. A lot of greyhounds can't be trusted in homes with cats. Does that mean they need to be put down or beaten until they are afraid of cats? No. That would be insane. They are placed in homes without cats and the owners are made aware that they will probably kill a cat if given the chance. That's it. Simple. Find the dog a home where there aren't things it wants to kill.