Drop out of Oxford and go to American university (4)
I believe the answer is:
omit
'drop out' is the definition.
(I've seen this before)
'american university' is the wordplay.
'american' becomes 'o' (I can't explain this - if you can you should believe this answer much more).
'university' becomes 'mit' (I've seen this in other clues).
'o'+'mit'='OMIT'
'of oxford and go to' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for omit that I've seen before include "Leave out or undone" , "Leave out or forget" , "Leave out, do not include (4)" , "Leave out, perhaps in error" , "Leave something out" .)