No need for a mass driver...
A simple spring loaded piston launching system should generate more than enough material to escape velosity. Use that to launch a few thousand tons of the object into different orbits and the remainig larger object should then be in an orbit that is much different than the original. Assuming of course that the spring powere piston launches are properly timed to focus the energy imparted into the larger object's orbit.
Alternative if you don't like littering space with all those boulders. Aim them at the Earth. keep the individual pieces small enough so that they burn up on entry.
Before you burn them up, of course you would first remove any valuable ores.