Wow, that's the first step!
However, the most efficient method would be actually land (I know - maybe even impossible?) on it, and use propellers to change its trajectory. We don't have too much throwaway high-tech to crash it on asteroids...
I'm not sure this is actually a necessary explanation...but while propellers technically COULD function in space (not a perfect vacuum, right?)...they're basically going to be useless.
Impact is actually a more efficient method, as it avoids the fuel consumption required for deceleration and soft landings.