the ability to destroy Earth would take a hell of a lot of power. Hell, even splitting off a decent chunk would take a lot of energy.
What would be possible is launch the world into a nuclear winter. Activate enough bombs and spread enough radiation and dust into the air. The dust would block most sunlight and the radiation would kill most anything that survives the cold and starvation (plants wouldn't be able to live in such cold)
of course, even creating a large enough force to get that much dust and debris into the atmosphere would take a lot of energy. Nuclear war could probably do it, but that would require that no one goes "Hey, wait, truce. We're just killing ourselves."