Cut out mixing lime in tea (9)
I believe the answer is:
eliminate
'cut out' is the definition.
(I've seen this in another clue)
'mixing lime in tea' is the wordplay.
'mixing' indicates an anagram.
'lime'+'in'+'tea'='limeintea'
'limeintea' is an anagram of 'ELIMINATE'.
(Other definitions for eliminate that I've seen before include "Completely remove, get rid of" , "defeat" , "Do away with, get rid of" , "put out" , "Remove from contention" .)