What is the meaning of "beat up" ?
They claimed they had been beaten up by the muggers after leaving the restaurant.

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To be "beaten up" in your example means to be physically assaulted.

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It means someone punched and kicked them.

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Beat up - give a beating to
Beat up - give a beating to; subject to a beating, either as a punishment or as an act of aggression; "Thugs beat him up when he walked down the street late at night".