The rocket equation is a bitch and it's one of the reasons that the folks planning to deflect an Earthbound asteroid of comet with a gravity tug really piss me off. They've spent decades promoting this approach and decrying other approaches yet they don't have an answer for how they plan to deal with the total dV they'll need to use a gravity tug. Think about it ... they would have to travel as fast as possible to intercept so the dV from Earth would need to be over 25Kmph just for the outbound leg. The asteroid or comet will be incoming at perhaps 25K-40Kmph so the total dV is now more like 50K-65Kmph. All of that just to arrive at the object and begin station keeping. In order to be effective as a tug it will need to have a non-trivial mass and that mass will have to be constantly moved to maintain station keeping requiring a lot of fuel. When you work through the rocket equation beginning with the mass of the tug when it arrives at station keeping then working backwards to launch and you have a rocket no one has ever seen or dreamt of. An Ion thruster might be useful for a gravity tug to maintain station keeping, but getting there will require conventional chemical rockets and more dV than feasible.
When all is said and done I think the only practical approach to deflecting a large asteroid or comet is to use stand-off detonations of nukes -- one or many. You don't have to blow it up, just dump a ton of energy on one side of it and let the enormous cloud of gasses that are ejected push by impulse. If one is not enough no problem -- send as many as needed with a few more spares. I single moderate size rocket (Falcon Heavy) could launch a bus/truck with a dozen 1MT or larger warheads with 25-30Kmph dV. No need to burn more fuel to reverse as you can detonate as it passes by.
Brian