The Town defender was dismissed in the 70th minute of the game for violent conduct.
Aswad will now miss the next three games against Hereford United, Gateshead and Welling United.
Meanwhile, Nathan Pond is set to play his last game for the Mariners against Hereford on Saturday. The Fleetwood player's loan with the club ends after Saturday's game and he is set to return to the Highbury Stadium.