you thinking like shockwaves or something?
there are no shockwaves in space tho
there are not enough particles to carry that energy, it will produce heat energy, so you might melt the asteroid
or do you mean like, nuclear propulsion or something
on the other hand we can just drill a BUNCH of nukes into the asteroid and blow that stuff up
with enough we can make small enough chunks that they wont affect us much at all