How to remove paint fallen on an existing watercolor painting with the least damage to the painting?
It's best to act quickly, and absorb the paint with either a cloth or (nearly) dry brush. You can remove most of the spilled paint that way.

Then, depending on what's still visible, you might want to wet the edges of the stain, to soften the colour transition. 
You might also want to repaint a part of the existing painting, or if you're really creative, give the stain a purpose in your painting. Like, when your painting is a still life with flowers, the unwanted drop of paint may become a bug or a hole in one of the leaves.