Second time university cut out what undergraduate did? (7)
I believe the answer is:
studied
'what undergraduate did?' is the definition.
(undergraduates study at university)
'second time university cut out' is the wordplay.
'second' becomes 's' (common abbreviation).
'time' becomes 't' (abbreviation).
'university' becomes 'U' (abbreviation for university).
'cut out' becomes 'died' (as in a machine cutting or dying out).
's'+'t'+'u'+'died'='STUDIED'
(Other definitions for studied that I've seen before include "Scrutinised" , "Learnt by reading" , "Read" , "Examined" , "Looked at closely" .)