The most common and most likely answer to this crossword clue is the 3 letter word GOB
I've seen this crossword clue in The Daily Telegraph
G
O
B
Buddy explains!
The straight part
We know that "Mug" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mug = gob.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GOB mean?
GOB noun- A lump of soft or sticky material.
- The mouth.
- Saliva or phlegm.
- A sailor.
- Waste material in old mine workings, goaf.
- A whoopee pie.
- To gather into a lump.
- To spit, especially to spit phlegm.
- To pack away waste material in order to support the walls of the mine.