Born in Chicago, Illinois, Mummery moved at an early age to Brandon, Manitoba. He first played senior-level hockey for Brandon YMCA in 1907–08. He moved to Fort William, Ontario to play a season with the Fort William Forts on the Northern Ontario League. He returned to the prairies playing for Brandon and Moose Jaw in minor professional leagues. In 1912, he joined the Quebec Bulldogs, then in the National Hockey Association (NHA). In his rookie season, the Bulldogs, the defending champions, won the NHA and Stanley Cup championships. He played with the Bulldogs until 1916, when he joined the Montreal Canadiens for a season. The Canadiens won the NHA title but lost to the Seattle Metropolitans in the Stanley Cup championship.