Cut the cackle and use the tea towel (3,2)

I believe the answer is:

dry up

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'towel' is the definition.
(thesaurus)

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

(Other definitions for dry up that I've seen before include "Lose moisture? -shut your mouth!" , "Shed moisture or stop talking" , "Desiccate" , "Cease talking" , "Use a tea towel?" .)

I've seen this clue in The Globe and Mail.

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