You are going to drop her as a friend. You are not going to see her any more.
It is a strong expression. It is "figurative;" it is a "metaphor." The idea behind it is that she makes you feel the way you feel if you get dirt on your hands. You not only want to stay away from her, but you feel as if you need to wash your hands.
Here "of" introduces the dirty thing that is on our hands. If we have melted chocolate on our hands, we "wash our hands of this chocolate." (We also say we "wash the chocolate off our hands.") To say "I've decided to wash my hands of her" means you are thinking of her as being like dirt that is on your hands.
There are a number of English idioms, expressions, and metaphors about dirty hands and washing hands. The idea is that if you stand aside and watch, your hands stay clean, but if you really take part and help, your hands get dirty.
This can be a good thing. "If you want to be a software developer, you can't just read about it. You have to get your hands dirty writing code."
If someone is part of a group doing something bad, "his hands are not clean in this matter." Someone decides to quit participating, for ethical reasons, might say "That's it. I won't do this any more. I am washing my hands of this."
The scientist, Robert Oppenheimer, felt guilty about developing the first nuclear weapon. He knew he was indirectly responsible for the deaths of hundreds of thousands of people, and he said to the president of the United States, "I have blood on my hands."