He played college football for the Stanford Cardinal and was selected by the Texans in the third round of the 2021 NFL draft.

Mills played in five games during Stanford's pandemic-shortened 2020 season, completing 129 of 195 passes for 1,508 yards with seven touchdowns and three interceptions.

[15] Due to incumbent starting quarterback Deshaun Watson being ruled inactive, Mills was named the second option behind Tyrod Taylor.

[16] He made his NFL debut during the second half of the Week 2 game against the Cleveland Browns after Taylor was injured, throwing for 102 yards, a touchdown, and an interception in the 31–21 defeat.

[20] In Week 4, Mills struggled against the Buffalo Bills, completing 11 of 21 passes for 87 yards and four interceptions in a 40–0 shutout defeat.

[26] Mills won his first NFL game during Week 15 against the Jacksonville Jaguars, completing 19 of 30 passes for 209 yards, two touchdowns, and an interception in the 30–16 victory.

[37] Mills appeared in six regular season games as well as the Texans' Wild Card win against the Browns in relief, completing 18 of 39 passes for 173 yards and two touchdowns.

[39] He appeared in four games during the 2024 regular season as Stroud's backup, primarily seeing most of his action in Week 18 with the Texans' playoff position secured.