Hoffman attended Shaker High School in Latham, New York, and played for their baseball team as a pitcher. In his junior year, he pitched to a 7–0 win–loss record. In Hoffman's senior year, he led Shaker High School to their first Section II Class AA title game since 2002 against town rival Colonie High School. Hoffman pitched seven shutout innings, 101 pitches and struck out nine. He struggled to be noticed by college baseball programs in the National Collegiate Athletic Association's Division I, as his fastball averaged. Hoffman pitched in Connie Mack Baseball during the offseason to attract attention from college programs, where his fastball improved to. This led to his signing a letter of intent with East Carolina University, a Division I school in Conference USA.
Hoffman was considered to be one of the best prospects available in the 2014 Major League Baseball Draft, with the potential to be selected first overall, before his injury lowered his draft stock. The Toronto Blue Jays selected Hoffman in the first round, with the ninth overall selection, and he signed with Toronto on July 2 for the full bonus slot value of $3.1 million. Though unable to pitch, Hoffman was assigned to the RookieGulf Coast League Blue Jays for the 2014 season. He began throwing off a mound in February 2015, and made his professional debut with the Dunedin Blue Jays of the Advanced-AFlorida State League on May 20. Hoffman's fastball reached during his first start. After making 11 starts with Dunedin, the Blue Jays promoted Hoffman to the New Hampshire Fisher Cats of the Double-AEastern League. He made his first start for New Hampshire on July 18, pitching a career-high innings and allowing two earned runs.
Colorado Rockies
On July 28, the Blue Jays traded Hoffman, José Reyes, Miguel Castro, and Jesús Tinoco, to the Colorado Rockies for Troy Tulowitzki and LaTroy Hawkins. Hoffman was assigned to the New Britain Rock Cats of the Eastern League following the trade. Hoffman began the 2016 season with the Albuquerque Isotopes of the Class AAAPacific Coast League. He was selected to appear in the 2016 All-Star Futures Game. Hoffman made his major league debut for the Rockies on August 20. Hoffman continued to remain in the rotation for the remainder of the season, finishing with a record of 0-4. The following season, he split time between the AAA level and the Rockies rotation. He was 6-5 with an ERA of 5.89 in 23 games, 16 starts. In 2018, Hoffman spent the majority of the season at the AAA level, only making 6 appearances for the Rockies. In 2019, Hoffman was 2-6 with a 6.56 ERA in 15 starts.