Clean up for the dog (3)

I believe the answer is:

mop

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'clean up' is the definition.
(I've seen this in another clue)

I don't understand how the rest of the clue works.

(Other definitions for mop that I've seen before include "Wet cleaner" , "It's used to wipe the floor" , "Implement for washing floor" , "Finish off a task - . . . up" , "Cleaning implement" .)

I've seen this clue in the Evening Standard.

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