If only we had an aether wave grappler beam to pull passing debris out of orbit.
Well, if the 21st century name for an "aether wave grappler beam" is a laser, then that might just be possible - have a look towards the end of this article http://www.space.com/35008-comet-strike-danger-to-earth.html
Rather than a grapple, this would be a deflector beam. The idea of using a laser for comets makes sense when you consider that blasting energy to icy bodies can result in jets of vapour or gases acting as thrusters on the comet, deviating its orbit.
Other than that, barring any jets, a body that needs to be deflected would presumably need to receive enough momentum from the colliding photos to actually deviate it's orbit.
I have heard of long term exposure to laser radiation which can over time significantly alter the orbit of an object, or propel an object through space. Generally speaking, the photon pressure is extremely low, but in the relative vacuum of space, and over long periods of time, the idea is the basis for probes or spaceships that could be accelerated to very high speeds, some significant percentage (say 25% of the speed of light). So it's possible that you could focus a laser long enough on a satellite to knock it's orbit. Buf off the top of my head I don't know how much pressure you can get from say a very intense burst or set of bursts of a laser beam.
Among some job applications for jobs involving secret government-sponsored research programmes, I have heard of projects which aim to concentrate ridiculously large amounts of energy in an extremely short duration laser pulse (directed energy weapons based on power amplification), which could actually vaporize, melt or otherwise push larger objects. But I need to do some calculations to see what is realistic or not (I'm definitely not an expert in the subject, so I'd have to re-invent the wheel and rely on my generalized knowledge starting from first principles)