Dismukes attended Spanish Fort High School in Spanish Fort, Alabama, where he played football and competed in track. He was a four-star recruit by Rivals.com and was ranked as the number one center in his class. He committed to Auburn University in April 2010 to play college football.
Dismukes started all 13 games at center as a freshman in 2011. As a sophomore in 2012, he started all 10 games he played in, missing two due to injury. Dismukes started all 14 games as a junior in 2013 and was a first team All-SEC selection. Dismukes entered his senior season in 2014 as a fourth-year starter. He again started all 13 games, winning the Rimington Trophy and being named a consensus All-American. He ended his career starting all 50 games he played in.
On May 2, 2015, Dismukes was signed as an undrafted free agent. On September 5, 2015, he was waived. On September 6, 2015, Dismukes was signed to the Steelers' practice squad. On September 8, 2015, he was released from practice squad.
On October 27, 2015, Dismukes was signed to the Panthers' practice squad. On November 23, 2015, he was released from practice squad. On November 24, 2015, he was re-signed to the practice squad. On February 7, 2016, Dismukes's Panthers played in Super Bowl 50. In the game, the Panthers fell to the Denver Broncos by a score of 24–10. On August 28, 2016, Dismukes was waived by the Panthers.
On December 28, 2016, Dismukes was signed to the Broncos' practice squad.