Wash one's hands and face, as in It's time to wash up for dinner. [First half of 1900s] Also see clean up, def. 2.
Clean the utensils after a meal, as in I'll cook dinner if you promise to wash up. [Mid-1700s] Also see do the dishes.
Bring about the end or ruin of; finish. This usage is often used put in the passive, be washed up, as in She's all washed up as a singer. [Colloquial; early 1900s]