2007-08: Kevin Czuczman made his debut in junior A hockey, appearing in two games with the Owen Sound Greys, and played for the Grey-Bruce Highlanders midget program near his hometown of Port Elgin.
2008-09: Czuczman played two games with the Greater Ontario Junior Hockey League's Listowel Cyclones; spending most of the season with the Junior C Walkerton Hawks in Ontario. He had no points nor penalties with the Cyclones. Czuczman scored 3 goals with 20 assists and 49 penalty minutes in 35 regular season games. In 10 playoff games he scored 2 goals with 3 assists and 4 penalty minutes as the Hawks won the WOJCHL championship.
2009-10: Overlooked by college hockey and major junior programs due to his size, Czuczman skated for the Waterloo Siskins in the Greater Ontario junior A hockey league. He scored 2 goals with 23 assists and 84 penalty minutes in 51 regular season games and had 1 goal, 1 assist and 15 penalty minutes in 10 playoff games.
2010-11: Czuczman, now 6'3" and 200 pounds, joined the Ontario Junior Hockey League's Newmarket Hurricanes. He impressed college scouts at the OJHL Governors Showcase in October and in November the 19-year-old committed to playing college hockey at Lake Superior State in 2011-12. In 47 regular season games with Newmarket he scored 4 goals with 19 assists and 40 penalty minutes. Czuczman scored 1 goal with 3 assists and 13 penalty minutes in 10 OJHL playoff games.
2011-12: Czuczman was one of four defensemen to play in all 40 games for Lake Superior State University in his freshman season. He scored 2 goals with 11 assists and was -1 with 26 penalty minutes. The Lakers finished seventh in the CCHA and swept Alaska in the first round before falling in back-to-back games to Western Michigan in the CCHA quarterfinals.
2012-13: Czuczman was invited to the Buffalo Sabres development camp over the summer before returning to Lake Superior State for his sophomore season. In 38 games he scored 2 goals with 9 assists and was +3 with 42 penalty minutes. The Lakers finished eighth in the CCHA and lost back-to-back games to Bowling Green after winning the first game of their first round playoff series.
2013-14: Czuczman made his NHL debut following his junior season at Lake Superior State — signing a two-year, entry-level free agent contract with the Islanders on March 11th, 2014 and skating over 20 minutes in the Islanders game at Minnesota one week later. Czuczman played in 36 games for the Lakers in what would be his final season of college hockey. He scored 10 goals with 11 assists and was -7 with 73 penalty minutes. Lake Superior State finished tied with Bemidji State for eighth in the newly-aligned WCHA but missed the playoffs based on tiebreaker criteria.
The Islanders signed Czuczman to a two-year entry-level contract on March 11th, 2014.