Deflection by Bola
Might be better to split the asteroid into two asteroids, wrap both asteroids in a net, connect them with a tether, and set them spinning like a bola. Once sufficient rotation is achieved, cut the tether connecting the two asteroids. They would go flying off in opposite directions, hopefully with enough delta-V to avoid hitting the Earth.
Complicated solution though.
A simpler solution would be to land a sling on the surface of the asteroid. Then start mining the asteroid, take the asteroid apart. Use the sling to whip the piece off into space. But the time the asteroid gets to Earth maybe there wouldn't be anything big enough to be a threat.