Follow due process. For cases where the evidence is overwhelming and incontrovertible, sentence the duly Convicted 2-legged animals to death by hanging. Screw the bleeding heart dribble about "they mustn't feel any pain; their death should be quick and painless", as the phrase "cruel and unusual" should only apply to truly tortuous deaths (think medieval dungeon)--NOT to execution methods used for hundreds of years by multitudes of nations.
Make sure the event is publicized.
Televise it.
All news channels.
Even animals can be cunning, and even animals can learn to predict consequences they don't want to suffer.
Even this action will not stop the drug crazed addled minds of the neanderthal.