Miller was born in Santa Clarita, California, and attended Canyon High School until age 16, when he transferred to Berkshire School in Sheffield, Massachusetts, and then played college hockey in Hockey East NCAA Division I for the University of Vermont Catamounts.

While with the Catamounts, Miller played 144 games, scoring five goals and 25 assists for 30 points, also serving as the captain of the team for the 2009–10 and 2010–11 seasons.

Emerging out of college, Miller signed an amateur tryout contract with the Providence Bruins of the American Hockey League (AHL) and played six games for the team during the regular season.

[4] He spent the full 2012–13 season with the Providence Bruins, playing 64 games and scoring 16 points and competing in the Calder Cup playoffs for the first time.

On January 21, 2014, Boston announced that they had re-signed Miller to a two-year, one-way contract extension.