You fly some nukes into it. Usually, at this point someone links to some NDT interview with Jon Stewart or something where he says "but if you blow up an aster

You fly some nukes into it. Usually, at this point someone links to some NDT interview with Jon Stewart or something where he says "but if you blow up an asteroid, the chunks will still hit you". Yes, well, if you blow up an asteroid the ratio of surface area to volume will change, and a greater percentage of the asteroid's mass will be