Wood accepted a football scholarship from Southern Methodist University. He was redshirted in 2011. He played in nine games in 2012, tallying five solo tackles, four tackle assists and half a sack. He played in 12 games, all starts as a 3-4 defensive end, in 2013, making 25 solo tackles, 24 tackle assists, one sack, one pass breakup, two forced fumbles, one fumble recovery and one blocked kick. Wood appeared in 12 games, all starts as a 3-4 defensive end, in 2014, registering 18 solo tackles, 22 tackle assists, 4 sacks and 1 fumble recovery. He played in 10 games with 9 starts in 2015 and was a team captain. He recorded 29 solo tackles, 10 tackle assists, 3.5 sacks, 2 pass breakups and 3 blocked kicks. Wood also spent time at long snapper in college. He finished his college career with 33-of-43 starts, 137 tackles, 22 tackles for loss, 9 sacks, 2 forced fumbles and 3 blocked kicks.
Professional career
Wood was rated the 85th best defensive end in the 2016 NFL Draft by NFLDraftScout.com.
Wood was signed as an undrafted free agent by the Dallas Cowboys after the 2016 NFL Draft, following a rookie minicamp tryout on May 24. During his first training camp with the team, he also played on the defensive line, even taking the snaps with the first defense in practices. He was waived on September 1, 2016. He signed a reserve/future contract with the Cowboys on January 16, 2017. In his second training camp with the Cowboys, he concentrated on being a long snapper and taking some of the practice load from stalwart L. P. Ladouceur. He was released on September 2, 2017.
In 2017, the New Orleans Saints couldn't find a potential candidate for the long snapper job during training camp. On August 28, the Saints obtained Jon Dorenbos from the Philadelphia Eagles in exchange for a seventh-round draft pick. On September 7, it was revealed that Dorenbos was diagnosed with an aortic aneurysm, which required immediate heart surgery. He was placed on the non-football illness list the same day, and released with an injury settlement on September 9, before announcing his retirement. On September 9, Wood was signed by the New Orleans Saints, after a last minute tryout that included four other players. He successfully became the team's long snapper for all punts and placekicks during the season. On February 20, 2018, he was re-signed to a one-year contract. On February 11, 2019, he was re-signed to a one-year contract. On March 23, 2020, Wood signed a four-year contract with the Saints.
