to remove the [excess] moisture from someone or something; to wipe someone or something with a sponge. The fight manager sponged his boxer down. I will sponge down the countertop.
To moisten or wipe the surface of someone or something with or as if with a sponge: The artist sponged down the canvas with primer before starting the painting. I had a high fever, so the nurse sponged my forehead down.