2009-10: Santeri Saari played one game for Jokerit's U18 team and was part of the U16 team that won the Finnish championship. He had no points or penalty minutes in his only U18 game. Saari scored 3 goals with 14 assists in 31 regular season games and had 5 assists in 12 U16 playoff games.
2010-11: Saari played three games for Jokerit's U20 team as a 16-year old, spending most of the season with the club's U18 squad, and played for Finland's U17 team in the 2011 Europe Youth Olympic Festival and World Hockey Challenge tournaments. He was +1 with no points and 2 penalty minutes in U20 play. Saari had 1 assist with 24 penalty minutes in 14 regular season games for the Jokerit U18 team and had 2 assists and 4 penalty minutes in nine playoff games. Skating in eight U17 games for Finland he had no points nor penalty minutes.
2011-12: Saari played 13 games for Jokerit in Finland's U20 SM-Liiga and was one of the top scorers from his defense spot with the club's U18 team. He had 2 goals and 2 assists and was +1 with 10 penalty minutes in U20 play. Saari scored 7 goals with 17 assists in 33 games for the Jokerit U18 team. Jokerit captured the U18 championship. Saari scored 3 goals with 2 assists and had 2 penalty minutes in 11 playoff games. He skated in 11 games for Finland's U20 and U18 teams but did not participate in the World Junior Championships at either level.
2012-13: Saari made his SM-Liiga debut, appearing in two games for Jokerit, and played in Finland's second league, Mestis, with Kiekko-Vantaa. He played most of the season with the Jokerit U20 team. He was +1 with no points nor penalty minutes, averaging 11:37 minutes of ice time in his two games for Jokerit. He had no points and was +1 with 6 penalty minutes in seven games for Kiekko-Vantaa. Saari was the third-leading scorer for Jokerit's U20 team, scoring 5 goals with a team-high 18 assists in 46 games, and was -5 with 34 penalty minutes. Jokerit finished 12th in the 16-team U20 SM-Liiga. Ranked 116th amongst European skaters in Central Scouting's final rankings Saari was selected by St. Louis in the sixth round (173rd overall) of the 2013 NHL Draft.