Irving grew up in Compton, California, but moved to San Jacinto as a youth and attended San Jacinto High School, where he played defensive tackle and tight end as a senior, recording 76 tackles, 7 sacks, 5 forced fumbles, 4 fumble recoveries, 19 receptions for 298 yards and 4 touchdowns. He accepted a scholarship from Iowa State University. He became a starter after switching from defensive end to defensive tackle as a junior, while posting 8 starts, 19 tackles and 2 sacks. He missed the entire 2014 season after being dismissed from the team following an incident at the VEISHEA festival. He finished his college career with 32 games, 44 tackles, 3 sacks, one forced fumble, one interception returned for a touchdown, 8 passes defensed and 3 blocked kicks.
On October 16, 2016, in a 30-16 win against the Green Bay Packers Irving was named NFC Defensive Player of the Week, when he forced three fumbles, recovering one, had a sack, and batted down a pass. Irving played only 19 snaps in the game. He was ejected from a game against the Cleveland Browns on November 6. In the fourth quarter of the week 15 game against the Tampa Bay Buccaneers, Irving had two tackles, one and a half sacks, 2 of his 5 quarterback pressures, a pass defended and a play where he hit quarterback Jameis Winston's arm just as he was releasing a pass that ended up being intercepted. Irving's play also led to Tampa Bay personnel and coverage changes that created opportunities for other Cowboys players, including rookie defensive tackle Maliek Collins sacking Winston with one minute left to play, which set up a game-sealing interception by cornerbackOrlando Scandrick. In the 2017 Divisional playoff game against the Green Bay Packers, Irving claims that in the final snap of the game the officials missed a holding call committed by guard T.J. Lang against him. During that play, Aaron Rodgers made a completion to Jared Cook with Cook's maintaining his feet a few inches inbounds from the sidelines. That completion set up a 51-yard Mason Crosby field goal to win the game with only three seconds on the clock.
2017 season
On March 6, 2017, Irving re-signed with the Cowboys. On May 23, it was announced that Irving would be suspended four games due to violating the league's performance enhancing drugs policy. He dropped his appeal and was officially suspended the first four games of the 2017 season. After joining the team, he was moved from defensive end to the three-technique defensive tackle position. He suffered a concussion in the twelfth game against the Washington Redskins, which was complicated by the fact that he kept playing through it. The lingering symptoms he experienced afterwards forced the team to declare him inactive for the rest of the season. Despite missing the first four games because of his suspension, and the final four because of a concussion, Irving still accrued seven sacks, 12 tackles, 19 quarterback pressures, 12 tackles, 6 passes defensed and one forced fumble. At the time of his concussion in Week 13, Irving was leading all defensive tackles in the NFL in sacks.
2018 season
On March 14, 2018, the Cowboys placed a second-round restricted free agent tender on Irving. On June 15, it was announced that due to violating the NFL's Policy and Program for Substances of Abuse, Irving would again be suspended for the first four games of the regular season. The Cowboys placed Irving on the reserve/did not report list on July 25 to start training camp, as he dealt with his off-field issues. He was added to the active roster on October 6 after serving his four-game suspension. Irving played in two regular season games, both in October, registering four tackles and one sack. He suffered a high ankle sprain during practice on November 1, and did not play again.
Retirement
On March 1, 2019, Irving was indefinitely suspended by the NFL for again violating the league's policy on substances of abuse. A few days later, he announced that he was quitting football because he was opposed to the NFL’s drug policy, specifically with regards to marijuana. Following this incident Irving became an activist for cannabis. He opened a cannabis business with a focus on CBD-related products. Irving co-founded his own cannabis advocacy magazine called Cannabis Passport.