2009-10: John Stevens played for Team Comcast in the Atlantic Youth Hockey League. In 34 games he scored 11 goals with 18 assists and 29 penalty minutes. Stevens was invited to USA Hockey's Select 16 Development Camp. He was selected by Plymouth in the eighth round (159th overall) of the 2010 OHL Priority Draft and was taken by Dubuque in the fourth round (60th overall) of the 2010 USHL Futures Draft.
2010-11: Stevens moved from New Jersey to Massachusetts to play for the Salisbury School in the New England prep school league. He scored 11 goals with 11 assists in 27 games as the Crimson Knights reached the semifinals of the NEPSIHA tournament; falling to runner-up Kent School, 5-4.
2011-12: Stevens made his USHL debut, appearing in two games with Dubuque in March, and was a team captain for Salisbury School in his senior season. He had no points and no penalties and was -2 with the Fighting Saints. Stevens scored 7 goals with 21 assists and had 16 penalty minutes in 28 games for Salisbury. The Crimson Knights entered the prep tournament as the top seed but lost in overtime to Lawrence, 3-2, in the semifinals. In March Stevens committed to playing college hockey at Northeastern in 2013-14. He was ranked 132nd amongst North American skaters in Central Scouting's final rankings prior to the 2012 NHL Draft but was not selected.
2012-13: Stevens skated for USHL champion Dubuque and participated in the 2012 USHL /NHL Top Prospects Game. In 59 games he scored 13 goals with 35 assists and was +8 with 14 penalty minutes. The Fighting Saints finished first in the Eastern Conference and defeated Fargo in the Clark Cup championship finals. Stevens scored 1 goal with 1 assist and was +3 with 6 penalty minutes in nine playoff games.
2013-14: Stevens played in all 37 games for Northeastern in his freshman season. He scored 7 goals with 15 assists and was -12 with 20 penalty minutes. The Huskies finished tied with New Hampshire for fourth place in Hockey East and lost to the Wildcats in a three-game playoff quarterfinal series.