Get beaten by mug, be humiliated (4,4)
I believe the answer is:
lose face
'humiliated' is the definition.
(I've seen this before)
'get beaten by mug' is the wordplay.
'get beaten' becomes 'lose'.
'by' means one lot of letters go next to another.
'mug' becomes 'face' (I've seen this before).
'lose'+'face'='LOSE FACE'
'be' acts as a link.
(Other definitions for lose face that I've seen before include "be shamed" , "Idle one's time away" , "get humiliated" , "Be embarrassed, humiliated" , "Suffer ignominy" .)