Is it possible to assassinate guards when saving a citizen

No, saving citizens doesn't do anything aside from creating monks and/or vigilante groups. However, you can then use these groups to your advantage. When you are trying to escape, you can run through a group of vigilantes to slow down the guards chasing you, giving you enough time to get to a rooftop and out of the city.

Monks can also give you a place to hide so that making an escape is simpler.

Then again, getting in huge sword fights is one of the best aspects of the game, so I always stuck around and tried to take out all the guards anyway.

Yes, it is required to kill all the guards at the scene, to save a citizen. After clearing off you need to speak with the saved citizen for accepting his/her help in the form of vigilantes or scholars as a confirmation of completing the task. That's why you cannot flee from the scene and expect the task to be completed.