Foutre au tapis is slang for the expression mettre au tapis which means literally “to put someone on the carpet / on the floor” (i.e. to put someone down). It originates in combat sports such as boxing where when you are au tapis, the referee starts to count and you are out if you don’t stand up before 10 is reached.
There is also aller au tapis which means to fall down in such a context.
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