When police arrived at the classroom, they found Christopher Krumm bleeding from self-inflicted knife wounds and taking his last breaths.
James Krumm was dead, Casper Police Chief Chris Walsh said.
"I can tell you the courage that was demonstrated by Mr. Krumm was absolutely without equal," he said, adding that the instructor's actions could offer some measure of comfort to those affected by the killings.
Authorities believe "around six" students were in the classroom when Christopher Krumm entered, Casper police spokesman Justin Smith said. No students were hurt.
Walsh said police still were trying to figure out what motivated Christopher Krumm to attack his father and Arnold, a math instructor at the college. Arnold died of multiple stab wounds.