Short was born in East Chicago, Indiana. He went to Central High School in East Chicago. There, he was a two-sport athlete playing both football and basketball. He was a high school teammate of E’Twaun Moore during basketball season, and the two led the Cardinals to the Indiana class 4A state title in 2007.

Short was rated as a three-star recruit and was rated the number 24 defensive tackle nationally by Scout.com. As a junior, Short recorded 80 tackles, 15 tackles for loss, and 8.5 sacks. As a senior, he registered 85 tackles, 9 sacks, 2 fumble recoveries, and 2 blocked punts. He committed to Purdue University on April 13, 2007. He was not heavily recruited as he did not land a scholarship offer from any other Football Bowl Subdivision schools.

Short attended Purdue University, where he played for the Purdue Boilermakers football team from 2008 to 2012. In 2009, Short started all 12 games and recorded 48 tackles, 4 tackles for loss, and was second on the team with 2 interceptions. He received Purdue’s Newcomer Award – Defense for spring practice, was named a freshman All American by CollegeFootballNews.com and was selected to the Big Ten All-Freshman team by the Sporting News. In 2010, Short finished fourth in the Big Ten in both sacks, with 6, and tackles for loss, with 12.5. He also led Purdue with 8 pass deflections, recorded 41 tackles, and blocked 2 kicks. He was named second-team All-Big Ten by the media. In 2011, Short was voted a captain by his teammates and started all 13 games. He finished with career highs of 54 tackles, 17 tackles for loss, and 6.5 sacks. He was able to record a tackle for loss in 10 of the 13 games he played. He also registered 1 forced fumble, 1 fumble recovery, 2 pass deflections, and blocked 2 kicks. In an overtime win against Ohio State, Short was named the Walter Camp National and Big 10 Defensive Player of the week after finishing with 3 sacks. He was named Purdue’s defensive MVP was named first team All-Big Ten by the media and second team All-Big Ten by the coaches.

He was a first-team All-Big Ten Conference selection in 2011 and 2012, and received second-team All-American honors from the Associated Press in 2012.

Short was drafted in the second round with the 44th overall pick by the Carolina Panthers in the 2013 NFL Draft. On May 22, 2013, Short signed a four-year $4.63 million deal. In his rookie year, Short played in all 16 regular season games. He recorded 30 tackles, 1 forced fumble, 1.5 sacks, and tied for second on the team with 21 quarterback pressures. He also finished tenth in the NFL in pass rush productivity among interior defenders, leading all rookies, and 16th in the NFL in run stop percentage. The Panthers finished first in the NFL with 60 sacks in 2013, second in points per game, and third in DVOA team defense. He was named to the All-Rookie Teams by PFF, ESPN, and SB Nation.

In 2016, Short started all 16 games for the Panthers, recording 55 tackles, 6 sacks, three passes defensed, and a forced fumble.

On February 27, 2017, the Panthers placed the franchise tag on Short. On April 17, 2017, Short signed a five-year, $80 million contract with the Panthers. He started all 16 games, recording 49 combined tackles, 7.5 sacks, and two forced fumbles.

In 2018, Short started 14 games, recording 42 combined tackles, three sacks, and a forced fumble.

On October 1, 2019, Short was placed on injured reserve with a partially torn rotator cuff.

On October 15, 2020, Short was placed on injured reserve after undergoing season-ending shoulder surgery.