He was selected by the Predators 23rd overall in the 2007 NHL Entry Draft. Turning professional in 2009, he spent parts of three seasons with the Predators' minor league affiliate, the Milwaukee Admirals of the American Hockey League (AHL), before joining the Predators. Internationally, Blum has represented Team USA on four occasions. He won silver at the 2006 Ivan Hlinka Memorial Tournament, and has competed in the 2008 and 2009 World Junior Championships, finishing without a medal both times. He also competed at the 2018 Winter Olympics, once again failing to medal.