I was in this situation before and the best thing that you can do is wait it out and see who is saying what. It's very said because those rumor mongers are the ones who spread the poison the fastest and you have become the person who runs around trying to justify your side of the story. At some point, when the moment is less heated, you'll be able to talk to the "accuser", unfortunately, you may not want to be friends with her at that point, anyway, depending on how much she made the decision to drag your name in the mud.
As far as her telling the mutual friend: Since you refer to her as a "friend", she has earned your friendship. If the friendship is that easy to break by listening to a bad rumor, it wasn't worth the friendship. Sadly, I have seen so many female adults resort to this "high school", juvenile, behavior of friendships, in my neighborhood. Personally, you must take a higher path. Just make sure that you pull your shoulders back, apologize if you have done ANYTHING wrong, but, don't get mixed into sharing your part of the "rumor" by talking against the other, because then you will be no better than the others.
Good luck.