"å vaske opp" means "to do the dishes" or "to wash up". "clean up" would be "rense opp", "rydde unna", "gjøre rent (i)". "vaske opp" has a very unambiguous meaning in Norwegian, and is not confused with other kinds of cleaning. "vaske" on its own, on the other hand, would be "wash" or "clean". I hope this made sense!
This comment is 6 months old already but since you never got an answer I figured I'd chime in haha. I'm American and for me, "washing up" makes me think of washing myself up, usually my face or hands. I'm specifically from New York, so I'm not sure if other parts of the country use "washing up" to refer to dishes or not.