Beasley attended Adairsville High School in Adairsville, Georgia, where he was a three-sport standout in football, basketball and track. He played as running back and linebacker for the Adairsville Tigers high school football team. He was named All-county and All-area in both his junior and senior seasons. As a junior, he totalled 57 tackles, two recovered fumbles and an interception, while also hauling in 15 receptions for over 200 yards. As a senior, he had 120 rushes for 828 yards with seven touchdowns on offense, and had 102 tackles (12 for loss) and an interception on the defensive side of the ball. In addition, he also had seven punt returns for a 17.3-yard average and two touchdowns, and also returned a kickoff return 80 yards for a score. He was named first-team All-state by Associated Press (AP) and Georgia Sportswriters Association. He also played in the Georgia North-South All-Star game, where he had a blocked field goal.
Beasley also competed in track & field while at Adairsville, where he competed mainly in sprints and jumps. At the 2010 GHSAA Regional 7-AA Championships, he placed third in the high jump (6-0 or 1.84m) and second in the triple jump (44-0 or 13.44m), while also earning a third-place finish in the 100-meter dash race after running a personal-best time of 11.14 seconds.
Considered a four-star recruit by ESPN.com, Beasley was listed as the No. 19 athlete in the nation in 2010. He was rated as the No. 37 athlete in the nation and No. 37 player in Georgia by Rivals.com. He was considered the No. 34 outside linebacker in the nation and No. 37 player in Georgia by Scout.com. Also an All-Southeast Region pick and the No. 33 player in the state according to SuperPrep. Beasley chose Clemson over Alabama, Auburn and Stanford.
Beasley was redshirted as a freshman in 2010. As a redshirt freshman in 2011, he played in nine games recording two tackles. As a sophomore in 2012, he recorded 18 tackles and eight sacks. Through the first six games of his junior season in 2013, he led the nation in sacks. He finished the year with 13. Beasley was a first-team All-Atlantic Coast Conference (ACC) selection and was named a consensus All-American.
Beasley opted to stay his senior year to finish his education instead of declaring for the 2014 NFL Draft. He was projected to have been picked up in the second round as predicted by the NFL's draft advisory board. Beasley entered the year with 21 career sacks, which was eight away from setting the all-time school record for career which was set by Michael Dean Perry and Gaines Adams at 28. In October he broke the record. He was named the ACC Defensive Player of the Year and was again a consensus All-American.