Dodd attended Riverside High School in Greer, South Carolina. As a senior, he had 78 tackles and nine sacks. He committed to Clemson University to play college football. Dodd spent a year at Hargrave Military Academy after graduating from high school. 
Dodd played in 24 games and had 20 tackles as a backup his first three years at Clemson from 2012 to 2014.  In 2015, Dodd became a starter for the first time and recorded 60 tackles and 12 sacks.   During Clemson's loss to Alabama in the 2016 College Football Playoff National Championship, he had seven tackles and three sacks.
|Ht||Wt||Arm length||Hand size||40‑yd dash||10-yd split||20-yd split||20‑ss||3‑cone||Vert jump||Broad|
| 6 ft 5 in |
| 277 lb |
| 34 in |
| 10 in |
|4.86 s||1.69 s||2.84 s||4.44 s||7.18 s|| 30.5 in |
| 9 ft 2 in |
|All values from NFL Combine and Pro Day |
Dodd was drafted on April 29, 2016 by the Tennessee Titans in the second round (33rd overall) of the 2016 NFL Draft. He recorded his first sack in his first full start against the Detroit Lions in Week 2 after replacing an injured Derrick Morgan.  He was placed on injured reserve on December 5, 2016 after re-injuring his foot from early in the offseason.