End a relationship. No longer responsible for something. No longer interested in someone. Suggests an earlier relationship which has now ended. Imagine painting a wall and then washing your hands afterward, you are done with it and no longer want to go back to painting it again. Also, phrases as ‘washed someone out of your hair’. (Compare to Wash out of your hair.)

“I don’t paint houses anymore, I’ve washed my hands of that kind of work.”