Composer who profits from the cuts (6)

I believe the answer is:

barber

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'composer' is the definition.
(Samuel Barber)

I cannot understand how the remainder of the clue works.

(Other definitions for barber that I've seen before include "producing various versions of Hair?" , "responsible for Hair?" , "Sweeney Todd's occupation in Fleet Street" , "Men's hairdresser, musically of Seville" , "Sweeney Todd's job" .)

I've seen this clue in The Sun.

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