Cut out part of a rude passage (6)
I believe the answer is:
deduct
'cut out part' is the definition.
'deduct' can be an answer for 'cut' (thesaurus). I am not sure about the 'out part' bit.
'a rude passage' is the wordplay.
'a rude' becomes 'de' (I can't explain this - if you can you should give a lot more credence to this answer).
'passage' becomes 'duct' (duct is a kind of passage).
'de'+'duct'='DEDUCT'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for deduct that I've seen before include "Make a subtraction" , "Remove" , "Subtract, take away" , "Withhold" , "Knock off" .)