Keep in mind I was speaking of moving asteroids.
Even if you build a trebuchet on an asteroid, the gravity that powers it will be minimal.
Rotational energy, on the other hand, depends on the power source, (preferably nuclear).
Pick up a rock, throw it in the direction opposite to the preferred direction of travel, and then repeat.
Nuclear-powered trebuchets? Gracious!
So, you would have to throw half the asteroid off the asteroid with your trebuchet to diminish its speed by half.