Mayza was drafted by the Toronto Blue Jays in the 12th round of the 2013 Major League Baseball draft. He received a $100,000 signing bonus and was assigned to the Rookie-levelGulf Coast League Blue Jays to begin his professional career. After three appearances in the Gulf Coast League, Mayza was promoted to the Rookie AdvancedBluefield Blue Jays of the Appalachian League. Mayza made 13 total appearances in 2013 and posted a 1–4 record, 7.76 ERA, and 27 strikeouts in 29 innings pitched. In 2014, he split time between Bluefield and the Short Season-AVancouver Canadians. In 26 innings, Mayza worked to a 2–4 record, 6.75 ERA, and 20 strikeouts. Mayza pitched the entire 2015 season with the Class-ALansing Lugnuts. He made 26 appearances for the Lugnuts, and posted a 3–2 record, 3.07 ERA, and 62 strikeouts in 55 innings pitched. Mayza continued to progress through the Blue Jays organization, beginning the 2016 season with the Advanced-ADunedin Blue Jays. In June, he earned a promotion to the Double-ANew Hampshire Fisher Cats, where he finished the year. Mayza made a career-high 42 pitching appearances in 2016 and went 3–3 with a 2.25 ERA and 65 strikeouts in 64 total innings. On January 19, 2017, Mayza was invited to Major Leaguespring training. He was assigned to Double-A New Hampshire to begin the 2017 season. After 29 appearances, Mayza was promoted to the Triple-ABuffalo Bisons. He made 11 relief appearances, posting a 0.93 ERA, before his first promotion to the Majors. On August 14, 2017, Mayza was called up by the Blue Jays. He made his major league debut on August 15, pitching a scoreless 9th inning in a 6–4 loss to the Tampa Bay Rays and recording his first major leaguestrikeout against Peter Bourjos. Mayza was credited with his first major league win on September 12, when he pitched the bottom half of the 9th inning before the Blue Jays walked off the Baltimore Orioles 3–2. Mayza split the 2018 season between the major leagues and the Buffalo Bisons. In 37 games for the Blue Jays, he posted a 2–0 record with a 3.28 ERA and 40 strikeouts over 35 innings. On September 13, 2019, in the 10th inning in a game against the Yankees, Mayza threw the ball behind Didi Gregorius and immediately crumpled to the ground in pain. The next day, it was revealed he had torn his UCL and would undergo Tommy John surgery. Mayza was outrighted off the Blue Jays roster on November 20, 2019.