I have hear "mug it up" to mean to get a lot to eat. Also it is used as "mug up" meaning the same thing. "I'm going to mug it up when I get home." "I can't wait to mug up at McDonalds."

Here, in this case, I think your second answer is right. The Free Dictionary says: to mug it up (US) (= grimace) → gesticular, and grimace is to make a face like you are in pain or disgusted Mug here, in Britain, is slang for a foolish person, e.g.: "John, you were a real mug lending him £500 - he won't give it back!"