Seth was drafted in the first round of the 2009 WHL Bantam Draft. He was taken 11th overall by the Everett Silvertips but later traded to the Portland Winterhawks. Seth was then taken with the fourth overall pick in the 2013 NHL Entry Draft by the Nashville Predators. In 2013, Seth played for the United States under-20 national team, which won gold at the 2013 IIHF World U20 Championship. Seth was traded to the Columbus Blue Jackets on January 6, 2016, serving as one of the team's alternate captains from 2018. On July 23, 2021, Seth was traded to the Chicago Blackhawks, joining his brother Caleb who had been traded to the Blackhawks earlier in the same month.