Matthew Boyd competed at Cooperstown Dreams Park with the Mudville Youth Baseball Club (WA) during Tournament 10 in 2002 and the Golden Eagles (WA) during Tournament 9 in 2003.

Matthew graduated from Eastside Catholic School (Sammamish, WA) where he excelled on the diamond as a pitcher. He spent his freshman year at Mercer Island High School (Mercer Island, WAS) and he was named the MIHS Rookie of the Year.

Following high school, Matthew attended and played baseball at Oregon State University (Corvallis, OR). At the conclusion of his junior year, he was drafted by the Cincinnati Reds in 2012 Major League baseball draft, however, he chose to stay in school to complete his degree. He did make the leap to professional baseball in 2013 when he was chosen by the Toronto Blue Jays in the 2013 Major League baseball draft. He made his Major League debut on June 27, 2015.

Shortly after making his first trip to the major league mound, Matthew was traded to the Detroit Tigers. Just prior to the 2022 season, Matthew signed a deal with the San Francisco Giants where played until August of the same season when he was sent to the Seattle Mariners. Matthew had a second stint with the Tigers from December of 2022 to June 29, 2024, he was then part of the Cleveland Guardians organization. Matthew and the Guardians clinched the 2024 American League Central division.

Matthew was traded to the Arizona Diamondbacks on December 21, 2024.