Sutton, who was handed the suspension Wednesday, was assessed a major penalty and game misconduct for boarding after hitting Dupuis with less than three minutes left in New York's 6-4 loss to the Penguins on Tuesday night.
Dupuis was down on the ice for several minutes before being helped to the Penguins' dressing room. He used a towel to cover up an apparent nose injury, and blood stains remained visible on the ice.
Sutton will miss Thursday's game against Florida and will sit Saturday against New Jersey, forfeiting more than $31,000 in salary. He's eligible to return Jan. 26 against Washington.