Slough is a formal verb used for the action of getting rid of something unwanted. It is usually used with off. Slough can also mean "to lose a dead layer of (skin)" or "to become shed or cast off."

// The editorial urges the mayor not to slough off responsibility for the errors in the report.

// The exfoliating cleanser promises to gently slough away dead skin cells.

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"Before she left her apartment, she gathered and washed some in a bowl. Then she drew a bath and soaked for a while, eating the figs one by one, swallowing even the hard stems. The steam and water loosened her tense muscles, and her aches started to vanish. She scrubbed herself until the dead skin sloughed off, and underneath, she was new." — Sally Wen Mao, Ninetails: Nine Tales, 2024

There are two verbs spelled slough in English, as well as two nouns, and both sets have different pronunciations. The first noun, referring to a swamp or a discouraged state of mind, is pronounced to rhyme with either blue or cow. Its related verb, which can mean "to plod through mud," has the same pronunciation. The second noun, pronounced to rhyme with cuff, refers to the shed skin of a snake (as well as anything else that has been cast off). Its related verb describes the action of shedding or eliminating something, just like a snake sheds its skin. This slough comes from Middle English slughe and is related to slūch, a Middle High German word meaning "snakeskin."