He played college football for the Purdue Boilermakers and signed with the Cleveland Browns as an undrafted free agent in 2019.

Following an injury to Matthew Stafford and Jeff Driskel, Blough started the final five games of the Detroit Lions' 2019 season.

[4] As a high-school athlete, he was being recruited by Purdue, Memphis, and New Mexico State after a junior season in which he completed 56 percent of his passes for 1,777 yards and 17 touchdowns against just three interceptions.

[10] In May 2013, Blough received a scholarship offer, and verbally committed to play college football at Purdue University following his visit on June 15, 2013.

[14] Blough redshirted his entire freshman season for the 2014 Boilermakers as sophomore Danny Etling was named the team's starter.

Blough was the backup on a roster that had just three scholarship quarterbacks, the other being true freshman Elijah Sindelar, who was recovering from a high school knee injury, and who Hazell wanted to redshirt.

Blough made his Purdue debut on September 12, 2015, throwing one incomplete pass in a three-and-out series in the closing minutes of a victory over Indiana State.

[16] Hazell ultimately decided to redshirt Sindelar during the 2015 season, resulting in Blough seeing playing time as Appleby's principal backup.

[18] Blough completed 29 of his 39 passing attempts for 340 yards and a pair of touchdowns, but the Boilermakers fell 28–35 to the Bowling Green Falcons.

Blough finished the final drive 2 for 8, including three straight incomplete passes to end Purdue's hopes at an upset.

[22][23] On November 14, Blough completed 26 of 45 passes for 287 yards with a touchdown and an interceptions as Purdue was narrowly defeated by #24 Northwestern.

Purdue's 2016 spring practice featured a quarterback battle between Blough and redshirt freshman Elijah Sindelar.

[55] On August 30, 2019, Blough was traded to the Detroit Lions in an exchange that also saw the teams swap conditional seventh-round draft picks.

[59] During the game he threw for his first NFL completion on a 75-yard touchdown pass to Lions wide receiver Kenny Golladay.

[60] In Week 14 at the Minnesota Vikings, Blough threw for 205 yards with one touchdown and two interceptions and was sacked five times in a 20–7 Lions loss.

[61] In Week 15 against the Tampa Bay Buccaneers Blough threw for 260 yards and 2 interceptions, one returned for a touchdown, in a 38–17 Lions loss.

[63] In Week 17 against the Green Bay Packers, Blough threw for 122 yards and an interception and caught a 19-yard touchdown pass from wide receiver Danny Amendola during the 23–20 loss.

[71] On December 14, 2022, Blough was signed off the Vikings practice squad to the Arizona Cardinals active roster.

[72] On December 30, Blough was named the starting quarterback for Week 17 against the Atlanta Falcons after Colt McCoy experienced a recurrence of concussion symptoms.

[75] On August 29, Blough was released by the Cardinals as part of final roster cuts before the start of the season.