Brian Mueller was a standout defenseman for Clarkson University from 1991 to 1995. During his time at Clarkson, he was a key contributor on three NCAA Tournament teams. Mueller was recognized for his excellent play, earning First-Team All-American honors in both his junior and senior seasons. He was also a two-time unanimous ECAC All-Star, and his legacy in college hockey was solidified when he was a top 10 finalist for the Hobey Baker Award in 1995. He finished his collegiate career with 39 goals and 117 assists in 131 games, which tied him for first all-time in assists among Clarkson defensemen.

After his college career, Mueller played professionally from 1995 to 2000. His career included time in various leagues, including the AHL, IHL, and ECHL. He played his first two professional seasons with the Springfield Falcons of the AHL before heading to Europe for a season. He later returned to North America and played in the UHL before retiring in 2000. He did not play in the NHL. After his playing career, Mueller went on to coach, winning two junior national championships.