The NHL suspended Gillies on Friday, two days after he was assessed major penalty for checking from behind and a game misconduct for hitting Clutterbuck, who had put Isles forward Justin DiBenedetto into the boards.
The incident occurred in Gillies' first game back after he sat out a nine-game suspension stemming from his elbow to the head on Pittsburgh's Eric Tangraadi on Feb. 11.
"From the play, the way I saw it develop, it was a hit from behind on DiBenedetto by the Minnesota player," Snow said prior to Saturday's game against St. Louis, the first of 10 Gillies will miss due to the suspension. "Trevor comes over and tries to finish his check. First point of contact was shoulder-to-shoulder. It was not a hit from behind by any means.
"I know Trevor as a person and I know there was no malicious intent when he was finishing the check."
Snow felt Gillies' status as a repeat offender might have been a consideration.
"Obviously he's coming off a nine-game suspension, he's got the rating as a repeat offender, but that's not really a question for me to answer," Snow said. "That's for Colin Campbell.
"I've said if before: Colin Campbell has a very difficult job," he added. "It's almost a situation where you can never win. We as an organization don't control suspensions or things of that nature."
Snow said there was no question of Gillies' popularity with the Isles' locker room and in the community.
"Trevor is one of the most popular teammates in that room," he said. "He's probably the frontrunner when it comes to community events or visiting hospitals and elementary schools. He has done great things for this community and Long Island."
Gillies will not be eligible to play again until the Islanders face Philadelphia on March 26.