Redirect asteroid by mining it for reaction mass?

[Lego_Prodigy]

You could alternatively try to shape the asteroid into a more desirable shape to shift the CoM into your favor.

[Steven P]

using the asteroid as reaction mass is the only low energy alternative.  This is the reason.

Disregarding the obvious practical problems, the lowest energy solution would be to push two halves of the asteroid apart.  The reason this is the lowest energy solution (excluding the energy needed to cut it in half) is because this least energy needed to change the momentum by a given amount.  This is because kenetic energy is proportion to velocity squared, but momentum is proportional to velocity.  You need to reach escape velocity with your thrust, but any additional speed is a waste of energy.  Unlike spacecraft, you have unlimited, free reaction mass.

In effect, the explosion of nukes near the surface has the same effect as my low velocity alternative, but is much more practical.  If you detonate without impact, it would heat one side of the object, causing part of its mass to propel it away from the explosion.  Nukes are the only energy source we currently have that could generate the necessary energy.