Diminished by taking a couple of minutes out? (5)
I believe the answer is:
minus
'diminished by' is the definition.
(I've seen this in another clue)
'a couple of minutes out?' is the wordplay.
'a couple of' becomes 'u' (I can't justify this - if you can you should give a lot more credence to this answer).
'minutes' becomes 'mins' ('min' can be a synonym of 'minute').
'out?' means one lot of letters goes inside another.
'u' put inside 'mins' is 'MINUS'.
'taking' is the link.
Can you help me to learn more?
(Other definitions for minus that I've seen before include "(Of temperature) below zero" , "Disadvantage" , "Lacking; below zero" , "Negative sign - negative thing" , "Lacking; negative" .)