Mullen grew up in the Hell's Kitchen neighborhood of New York. He and older brother Joe Mullen played roller hockey in the streets of Manhattan as children. After landing a job as a stick boy for the New York Rangers, he and Joe were offered a spot on a junior league team coached by Ranger head coach Emile Francis. Brian won an athletic scholarship to the University of Wisconsin-Madison where he played under legendary college hockey coach "Badger" Bob Johnson.