Cardinals coach Bruce Arians opened his news conference after Wednesday's practice by telling reporters they could read about the roster change and that he wouldn't talk about it. But Arians later said releasing Floyd was a unanimous decision by him, general manager Steve Keim and team president Michael Bidwill.
"It's a statement," Bidwill said from the NFL owners meetings in Irving, Texas. "We had a difficult decision to make there."
"Coach Arians talks to all of the team after games, before bye weekends and around holidays," Bidwill added. "He always makes sure that he emphasizes what our standards are, which is don't be 'the guy.' And also to be focusing on what you're supposed to be doing for the team."
Floyd was found unconscious behind the wheel of his running vehicle at a Scottsdale intersection early Monday morning, police said.
Floyd's black Cadillac Escalade sat through at least two green-light cycles with him passed out behind the wheel. Officers barricaded his SUV between their cars as they prepared to wake him up, according to the police report detailing the arrest.
The SUV's engine was running and Floyd's foot was on the brake, the report said.
The mood was somber in the Cardinals' locker room Wednesday as news spread of Floyd's release. A common refrain was how well-liked Floyd was.
"It's a tough day," quarterback Carson Palmer said. "Mike's a close friend of mine, offseason golfing buddy, workout partner, so it's tough. I believe in Mike. I hope for nothing but the best for Mike and look forward to seeing what he does with the next opportunity he gets."
Safety Tyrann Mathieu said he hoped Floyd gets another chance.
"Everybody is going to have something to say," Mathieu said. "Everybody is going to try to criticize you. Everybody thinks they know what you're going through. I think the most important thing is for him to believe in himself."
According to the police report, Floyd initially told officers that he was leaving his home in Scottsdale to pick his nephew up from the airport, but his story evolved into him having one drink, and he later said it was two drinks.
Police said Floyd's story jumped around between him drinking on the team plane back from Miami and drinking at the W Scottsdale Hotel, but Floyd eventually "settled" on having had wine -- "house cabernet" -- on the team plane. Floyd also told the officers he was on a blood-thinning medication.
Floyd had three alcohol-related brushes with the law at Notre Dame, including a DUI in his final season.
The Cardinals chose Floyd in the first round of the 2012 draft, 13th overall. He was playing this year under a team option that the Cardinals enacted before the 2015 season.
This season, his contract year, Floyd had 33 catches for 446 yards and four touchdowns. Those numbers were well off his 2015 stats, when he overcame early injury problems to catch 52 passes for 849 yards.
Floyd's best season was 2013, when he had 65 catches for 1,041 yards. He caught two passes for 18 yards in Arizona's 26-23 loss at Miami on Sunday.
The Cardinals host the New Orleans Saints at University of Phoenix Stadium on Sunday.
ESPN staff writer Eric D. Williams and The Associated Press contributed to this report.