Hammons first attended Carmel High School, where he averaged 8.3 points and 7.8 rebounds as a sophomore, earning honorable mention Associated Press accolades. In his junior season, he transferred to Oak Hill Academy, where as a senior, he averaged 7.0 points, 6.8 rebounds and 4.0 blocks per game.
When he graduated, he was given a four-star rating by Scout.com and by Rivals.com.
Hammons was named to the Big Ten All-Freshman Team at the conclusion of his first season playing for the Boilermakers, where he averaged 10.6 points, 6.0 rebounds and 2.0 blocks per game. At the conclusion of his sophomore season, Hammons had an average of 10.8 points, 7.4 rebounds and 3.1 blocks per game. He was awarded Honorable Mention All-Big Ten as well as being named to the Big Ten All-Defensive Team. He was named second-team All-Big Ten as a junior and was again awarded a spot on the Big Ten All-Defensive Team.
In his senior season, Hammons averaged 15.0 points, 8.2 rebounds, 2.5 blocks and 1.1 assists while shooting .592 from the floor. That season, he was named the 2016 Big Ten Defensive Player of the Year, first-team All-Big Ten, and was again named to the Big Ten All-Defensive Team. He was named to the 35-man midseason watchlist for the Naismith Trophy and was named one of the five finalists for the Kareem Abdul-Jabbar Award.
On June 23, 2016, Hammons was selected by the Dallas Mavericks with the 46th overall pick in the 2016 NBA draft. On July 8, 2016, he signed with the Mavericks and joined the team for the Las Vegas Summer League. During his rookie season, he had multiple assignments with the Texas Legends of the NBA Development League. He also had three 9-point efforts with the Mavericks during the season, to go with a season-best 7 rebounds on April 7, 2017 against the San Antonio Spurs.
On July 7, 2017, Hammons was traded to the Miami Heat in exchange for Josh McRoberts, a 2023 second round draft pick and cash considerations.
The son of Tyrone and Alfreda Hammons, he has a brother, Tyrone. He majored in organizational leadership and supervision.