The act of getting a hand job. Often resulting in an uncomfortable "tugging" of one's cock. Usually unpleasant.
Guy 1: "Did you fuck that slut last night?"
Guy 2: "No, I had to settle for the 'ol tug mcgraw"
Guy 1: "You should have told that bitch that a 'hand job is a man's job, but YO job is a BLOW JOB'."
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When a woman is knocked up by a professional athlete on a road trip
Maybe it is his kid. He could have Tug McGrawed her on his last road trip to Dallas.