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An abbreviation of the term "Gangsta Rap Made Me Do It", originating from Ice Cube's song of the same name. It essentially means "My bad, it wasn't my fault."
Paul: Ow! Why'd you slap me with your cock, then call me gay?
Jim: GRMMDI, dude.
Paul: Oh. We cool.
by Jumpin' JC August 24, 2010