If an asteroid is a threat to Earth

Instead of blowing it up, which might result in it reaggregating in a matter of hours,

If a sizeable asteroid is found heading towards Earth, one option is to nuke it. But too small a bomb would cause the fragments to fly apart only slowly, allowing them to clump together under their mutual gravity.

http://www.newscientist.com/article/mg20527514.700-terminator-asteroids-could-reform-after-nuke.html

mine it out of existence instead!

http://www.physorg.com/news187550107.html