2009-10: Saku Salminen skated for the HIFK U18 and U16 teams in Finland and played eight games for Finland's U16 team. Playing for HIFK's gold medal-winning U18 team he scored 8 goals with 10 assists and had 22 penalty minutes in 25 games. He scored 4 goals with 1 assist and 2 penalty minutes in 11 playoff games. Salminen played 15 games for HIFK's U16 squad, including six playoff games, and scored 12 goals with 15 assists and 58 penalty minutes. He had 1 goal and 6 penalty minutes skating for Finland's U16 team.
2010-11: Salminen played 13 games for HIFK in Finland's U20 SM-Liiga as a 16-year-old and was with the club's U18 team. He scored 2 goals with 2 assists and was +2 with 2 penalty minutes for the U20 team. In 16 games with HIFK's U18 team he scored 7 goals with 9 assists and 30 penalty minutes and had 1 assist and 6 penalty minutes in four playoff games. Salminen played for Finland's U17 team; scoring 1 goal in three games at the 2011 Europe Youth Olympic Festival and scoring 5 goals with 4 assists in 14 international games.
2011-12: Salminen went from HIFK to crosstown Helsinki rival Jokerit and represented Finland in the 2012 U18 World Junior Championship. Playing for Jokerit's U20 team he scored 9 goals with 17 assists in 44 games and was +11 with 16 penalty minutes. Jokerit lost to HIFK in the U20 SM-Liiga finals and Salminen had 1 assist and was +1 with 2 penalty minutes in 12 playoff games. He played four games with Jokerit's U18 team and had 1 goal with 1 assist and 4 penalty minutes. In seven games at the U18 WJC he had 5 assists and was +1. Finland advanced to the bronze medal game, falling to Canada.
2012-13: Salminen made his pro hockey debut, skating for Jokerit in the SM-Liiga and Kiekko-Vantaa in Mestis, and played for Finland's U20 team at the 2013 U20 World Junior Championship. Salminen opened the season with Jokerit, skating in twelve games before being loaned to Kiekko-Vantaa, and also appeared in one SM-Liiga game in December. He scored 1 goal with 1 assist and had an even plus/minus with 12 penalty minutes; averaging 10:44 minutes of ice time in 13 SM-Liiga games. In 16 games for Kiekko-Vantaa, including four games in the relegation playoffs to avoid demotion, Salminen scored 2 goals with 9 assists and was +7 with 2 penalty minutes. Playing in a lower line, checking role for Finland at the WJC, he was -1 with no points in six games. Salminen was ranked 74th amongst European skaters in Central Scouting's final rankings and was selected by Tampa Bay in the seventh round (184th overall) of the 2013 NHL Draft.