Stoutmire was selected in the seventh round (224th overall pick) of the 1997 NFL Draft by the Dallas Cowboys. As a rookie, he played strong safety in the nickel defense and displayed excellent run-support skills. When Darren Woodson sustained a knee injury, he started against the Philadelphia Eagles and registered 13 tackles—the first time a rookie started at safety for the Cowboys in a nonstrike game since Michael Downs in the 1981 season. He produced 7 special teams tackles, 2 interceptions (tied for the team lead), 2 sacks, 2 passes defensed, one forced fumble and was sixth on the team and seventh for NFL rookies in tackles with 76.
