Sometimes they can mean the same thing, but often they do no. "Clean up" is usually used for some problem that has to be resolved or some behaviour that has to be changed. "Tom is the one who made the mistake on the contract. I refuse to clean up his mess" = I refuse to deal with the problems he caused. "Anne really needs to clean up her act." = she needs to change her behavior for the better. "Clear up" means more to make something that is confused more understandable. "His explanation cleared up a lot of the confusion surrounding the proposed bill in the Senate,."