"Wiping down" something means wiping it with a rag, a towel, or a paper towel to clean it.

The killer wiped down everything she had touched to get rid of any fingerprints.

We use the phrase "wipe down" when we talk about the objects that you're wiping: a table, a car, a stove, etc.

We use "wipe up" when we're talking about getting rid of something messy:

Can you wipe that up, please?