Miss Ohio snubbed Senator Romney (4)
I believe the answer is:
omit
'miss' is the definition.
(synonyms)
'ohio snubbed senator romney' is the wordplay.
'ohio' becomes 'o'.
'snubbed' means to remove the last letter (could historically mean cutting the end off).
'senator romney' becomes 'mitt' (US senator Mitt Romney).
'mitt' with its last letter taken away is 'mit'.
'o'+'mit'='OMIT'
(Other definitions for omit that I've seen before include "Leave out or overlook" , "Don't include" , "Take out" , "Leave out or exclude" , "Leave out or forget" .)