Cleaner ticks off mourner (6-7)

I believe the answer is:

carpet-sweeper

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'cleaner' is the definition.
(I've seen this before)

'ticks off mourner' is the wordplay.
'ticks off' becomes 'carpets' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'mourner' becomes 'weeper' (weeper is a kind of mourner).
'carpets'+'weeper'='CARPET-SWEEPER'

Can you help me to learn more?

(Other definitions for carpet-sweeper that I've seen before include "Domestic appliance for picking up dust" , "Cleaner" .)

I've seen this clue in The Independent.

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