Coach Gus Malzahn made those announcements Friday after the defending Southeastern Conference champions finished their first practice of preseason camp. He didn't say how long Marshall or Mincy will remain on the bench against the Razorbacks on Aug. 30.
Marshall was cited for possession of less than an ounce of marijuana and a window tint violation during a July 11 traffic stop in Georgia. His mother paid the $1,100 in fines.
Mincy, who has 29 career starts, was arrested and charged with second-degree possession of marijuana in June.
''I've decided that they will not start Game 1 as part of their punishment,'' Malzahn said. ''I will say this: Nick Marshall is still our quarterback. Jonathon Mincy is still our cornerback but that's part of their punishment.''
That means sophomore Jeremy Johnson will start his second career game and first against an SEC opponent. Malzahn said he and offensive coordinator Rhett Lashlee had planned all along to give Johnson a bigger role, but that Marshall remains the starter. The senior worked with the first-team offense during the portion of practice open to the media.
Malzahn wouldn't elaborate on the players' punishment beyond losing the opening game start.
''That's part of the punishment,'' he said. ''The rest is between us.''
Marshall led the Tigers into the national championship game in his first season after transferring from junior college. He passed for 1,976 yards and ran for 1,068, accounting for 26 touchdowns while helping turn the zone read into Auburn's signature play.
Johnson completed 71 percent of his passes for 422 yards and six touchdowns against two interceptions.
''We're still going to keep on doing what we're doing. We're not going to stop for anybody,'' wide receiver Ricardo Louis said. ''Whether he's here or not, we're still going to be together as a team and try to win the games.''
Marshall has addressed the team after the incident, when he was not arrested.
''He's apologized about it, said he'll never do it again,'' Auburn receiver Ricardo Louis said. ''I can see he's sincere about it. For me, he doesn't show that it's affected him at all. He's out there making throws and making plays. That shows me that it doesn't affect him at all. He's a leader.''
Losing Kozan is a big blow for the offensive line, which returned four starters but lost No. 2 overall NFL draft pick Greg Robinson at left tackle. T
Kozan had back surgery after a weightlifting injury at home in Colorado this summer, Malzahn said. The third-year sophomore started every game last season and was a second-team preseason All-SEC pick.
''Obviously it's a terrible situation and we have to continue to work as a group of five as an offensive line,'' center Reese Dismukes said. ''He'll be there to support us and wish us nothing but the best.''