Grossman's professional career began in the Swedish Elite League during the 2003-04 season with Södertälje SK as a right wing. However, Grossman only notched two career points in the SEL, both assists, over two seasons. Even so, he was drafted by Dallas in the 2004 NHL Entry Draft in the second round with the 56th overall pick.
Grossman's professional debut in North America came on October 8, 2005, with Iowa. It was then that Grossman was converted to a regular defenseman, a move that led to Grossman being named Iowa's Most Improved Player after his rookie season.