The Joker is a master planer, edward is not made of rock, he can be killed, decapitated him and he die, if you have any problem the joker makes other vampires kill edward, i mean, from what i saw that imitation of Drusilla and darla is assembling an army but the joker would sertainly make them kneel, also he only need to kidnap Bella or use Jacob to kill edward, it's very simple, the joker would easily find a way to put his plan into moton.