Irving will miss the first four games because of violating the NFL's substance abuse policy. In 2017, he missed the first four games for violating the performance-enhancing drug policy.
It continues a tumultuous offseason for Irving. In April, a former girlfriend accused him of domestic violence and later recanted the story. Frisco, Texas, police concluded an investigation and did not press charges, but the NFL is also looking into the allegation.
Irving has also gained custody of his young daughter in the past months.
Irving had what was termed "sporadic" attendance at the Cowboys' offseason program, from the captains' workouts before the official program through the organized team activities. He attended the three-day mandatory minicamp that concluded Thursday but did not practice. Instead, he worked off to the side on his conditioning.
"I wasn't here because I chose not to be here," Irving said after Thursday's practice. "If I could've come, I would've. The real reason's none of the public's business."
The Cowboys put the second-round tender on Irving as a restricted free agent before the offseason began, worth $2.91 million.
As a result of the suspension, Irving will forfeit roughly $685,000 in salary. Last year's suspension cost a little more than $150,000 in salary. Under terms of the substance-abuse policy, Irving will be able to take part in training camp and the preseason games. Once the regular season starts, he will be able to continue to work out at The Star but not take part in meetings or practices.
He will be able to return Oct. 1 after the Cowboys play the Detroit Lions on Sept. 30.
Irving finished second on the Cowboys last season with seven sacks in eight games. In addition to the suspension, he missed the final four games with a concussion.
"There's more to my life than just football," Irving said. "I'm actually a real person. I have family issues, a lot of issues I've been dealing with. I can't go into much detail. Just know it's behind me. By the time the season starts, I won't be dealing with any of this BS anymore."