Blashill was born in Detroit, Michigan, but grew up in Sault Ste. Marie. He played college ice hockey as a goaltender at Ferris State University for the Bulldogs from 1994 to 1998. He earned team Rookie of the Year honors in 1994 and was named to the Central Collegiate Hockey Association (CCHA) All-Academic Team in 1997. Prior to his collegiate career, Blashill played at the junior level for the Des Moines Buccaneers of the United States Hockey League (USHL) from 1991 to 1994.

After his playing career ended, Blashill joined Ferris State’s Bulldogs team as an assistant coach in 1999. He remained there for three seasons before joining Miami University as an assistant coach for the RedHawks in 2002.

In 2008, Blashill was named head coach and general manager of the Indiana Ice, a Tier 1 junior hockey team in the USHL. In his first season, the Ice won the Clark Cup as USHL champions.

Blashill was later named head coach of Western Michigan University’s Broncos team on April 6, 2010. In his first season as head coach, Blashill led Western Michigan to a top-four finish in the CCHA, the CCHA Championship game and the 2011 NCAA Division I Men’s Ice Hockey Tournament, the most successful season for the University in 15 years. After the season, he was named USCHO Coach of the Year, Inside College Hockey Coach of the Year and College Hockey News Coach of the Year.

In July 2011, after one season at the helm of the Broncos, Blashill accepted an assistant coaching position with the NHL’s Detroit Red Wings under head coach Mike Babcock.

On June 25, 2012, it was announced that Blashill would become the head coach of the Grand Rapids Griffins, the top minor league affiliate of the Red Wings in the American Hockey League (AHL). He replaced Curt Fraser, who had accepted an assistant coaching position with the Dallas Stars of the NHL. Blashill was replaced on the Red Wings staff by NHL veteran assistant Tom Renney.

On June 18, 2013, the Griffins under Blashill won the Calder Cup as AHL champions for the first time in club history.

On June 4, 2014, it was announced that Blashill had agreed to a new three-year contract with the Red Wings organization through to the 2016–17 season to coach the Griffins.

With a win over the Rockford IceHogs on April 1, 2015, Blashill became the first coach in Griffins franchise history to post three 40-win seasons and three 90-point seasons. In three seasons with the Griffins, he compiled a 134–71–12–11 regular season record and won seven of nine AHL playoff series. He is the only coach in Griffins history to qualify for the Calder Cup playoffs in three consecutive seasons.

Following the departure of Detroit head coach Mike Babcock to the Toronto Maple Leafs, Blashill was named head coach of the Red Wings on June 9, 2015. On April 2, 2019, the Red Wings announced they signed Blashill to a two-year contract extension.