Hartman was born in Hilton Head Island, South Carolina, but grew up in West Dundee, Illinois, as a fan of the Chicago Blackhawks. After two seasons with the U.S. National Team Development Program and one with Plymouth of the Ontario Hockey League, the Blackhawks selected him in the first round (No. 30) of the 2013 NHL Draft.

After returning to Plymouth for the 2013-14 season, Hartman helped the United States win gold at the 2013 IIHF World Junior Championship. He spent most of the 2014-15 season with Rockford of the American Hockey League but got a five-game callup with the Blackhawks, making his NHL debut against the New Jersey Devils on Feb. 13, 2015.

He returned to Rockford in 2015-16, playing three games with the Blackhawks. But he made the jump to a full-time NHL player in 2016-17, finishing with 31 points (19 goals, 12 assists) in 76 games. He had 25 points (eight goals, 17 assists) in 57 games with Chicago before being traded to the Nashville Predators on Feb. 26, 2018.

Hartman was on the move again almost exactly a year later; he was traded to the Philadelphia Flyers on Feb. 25, 2019. He played 19 games with the Flyers before becoming a free agent and signing with the Minnesota Wild on July 1, 2019.

Hartman signed a three-year, $12 million contract with the Wild on Oct. 7, 2023.