To Wipe
To Mop Up
transitive verb, godan verb
You have the kanji for wipe, and this is the verb version of that, which makes this to wipe or to mop up.
You've already learned 拭く, which is a general word for the act of wiping, whether you're wiping a table or wiping your forehead. 拭う, on the other hand, is more commonly used in writing to describe the act of wiping away and removing something specific like sweat, tears, filth, or even doubts.
This is a verb, so it uses the kun'yomi. However, to differentiate this verb from 拭く, it uses a different reading, so here's a mnemonic to help you remember this:
What are you trying to wipe? Some nude goo (ぬぐ)! You spilled nude goo all over your floor, and now you have to mop it all up… pesky nude goo.
うちの子、まだ口をそでで拭うクセがあるんです。
My child still has the habit of wiping their mouth with their sleeve.
男はシャツで血を拭うと、また走り出した。
After wiping the blood with his shirt, the man started running again.
彼女はハンカチでなみだをそっと拭うと、決心したように立ち上がりました。
After gently wiping away her tears with a handkerchief, she stood up as though she had made a resolution.