Well earths escape velocity is about 11.2km/s, and the moon has a mass of 7.36 × 10^22 kg, with a velocity of 3,700kmph (1030m/s). That means you'd need about 3.806x10^30 J of energy to knock it out of orbit. That's about 910 exatons TNT, quite a long way short of a yottaton TNT. That's assuming it's entirely kinetic energy, if you used a bomb a large ammount of it would be released as radiation, you might be much closer to a yottaton of TNT required.
The energy required to 'destroy' or 'dismantle' the moon is alot harder to calculate, since it's not a clear definition. Simply breaking it in two won't permanantly destroy it, given a bit of time the gravity of the two will make them collapse back into a moon (altho this may take a looong time to settle down, I imagine the two parts would 'bounce', when the two parts merge they'll throw alot of material back out, it could take 1000s of years to become a sphere again). You could consider the moon 'dismantled' if half of it was thrown out of orbit, which would simply be half the energy as before (so about 455 exatons TNT).
How you would achieve either of these would be interesting, some good ideas are suggested in
How to Destroy The Earth Good luck on destroying the moon, I look forwards to it!