2009-10: Scott Savage played for the Los Angeles Selects and participated in USA Hockey's Select 15 Player Development Camp. He was selected by Vancouver in the ninth round (184th overall) of the 2010 WHL Bantam Draft. In August he committed to playing college hockey at Boston College in 2013-14.
2010-11: Savage played for the Los Angeles Selects U16 midget team. He scored 4 goals with 20 assists and 37 penalty minutes in 31 games. In March it was made official that he would be skating for the National Team Development Program's U17 team in 2011-12.
2011-12: Savage moved to Ann Arbor to skate for the USA Hockey National Team Development Program's U17 team. He scored 3 goals with 11 assists and had 34 penalty minutes in 69 games. Playing for the USA at the 2012 U17 World Hockey Challenge he had 3 assists and 2 penalty minutes in five games as the USA captured a silver medal.
2012-13: Savage played for the NTDP's U18 and U17 teams in his second season in Ann Arbor. He played 55 games with the NTDP U18 team and scored 1 goal with 7 assists and 14 penalty minutes. In five games with the U17 team he scored 2 goals and had 17 penalty minutes. Savage was not among the 210 North American skaters in Central Scouting's final rankings prior to the 2013 NHL Draft and was not selected.
2013-14: Savage was one of three freshman defensemen to see significant action for a Boston College team that was one of the top teams in the country. He skated in 35 of 40 games for the Eagles, scoring 4 goals with 14 assists, and was +13 with 12 penalty minutes. BC was 17-0-2 in its final 19 regular season games, finishing first in Hockey East, before falling to Notre Dame in a best-of-three series Hockey East quarterfinal series. The Eagles defeat Denver and Massachusetts-Lowell to win the NCAA Northeast Regional and lost 5-4 to national champion Union in the Frozen Four semifinals.