Mueller was acquired by the New Jersey Devils in a trade with the San Jose Sharks on June 17, 2017. The defenseman's first season in New Jersey was limited to 28 games because of a fractured clavicle, but he returned in time to help New Jersey to its first appearance in the Stanley Cup Playoffs since 2012.
Mueller, a native of Winterthur, Switzerland, played two seasons with Everett of the Western Hockey League. He was chosen by the Sharks with the No. 18 pick in the 2013 NHL Draft and signed a three-year contract with San Jose on Sept. 22, 2013. Mueller played 39 games with the Sharks in his rookie season of 2014-15, but spent most of the next two seasons with San Jose of the American Hockey League before being traded to the Devils.