Tinordi was committed to University of Notre DameFighting Irish of the Central Collegiate Hockey Association for the 2010–11 season. On August 10, 2010 it was announced that Tinordi would play for the London Knights of the OHL for the 2010–11 season, forgoing his NCAA eligibility. On March 16, 2013, he played his first NHL game against the New Jersey Devils, scoring his first NHL career point when his shot was deflected behind Johan Hedberg by Tomas Plekanec at 06:49 in the third period. The Canadiens would go on to win the game 2-1. In the 2015–16 season, Tinordi, no longer waiver-exempt, made the Canadiens roster out of camp as a reserve defenseman. With the Canadiens producing the league's best start to the season, Tinordi failed to feature in a game in the opening months of the season. On November 26, 2015, he was assigned to new AHL affiliate, the St. John's IceCaps, on a conditioning stint appearing in 6 games. In his return to the Canadiens, Tinordi featured in only three games in the following two months then on January 15, 2016 he was traded to the Arizona Coyotes in exchange for Victor Bartley and John Scott. On March 9, 2016, the NHL announced that they had suspended Tinordi for 20 games, without pay, for violating the terms of the NHL/NHLPA Performance Enhancing Substances Program. In a statement released by the NHLPA, Tinordi stated: "I did not knowingly take a banned substance. I understand, however, that I am responsible for what enters my body as a professional athlete and I accept the suspension. I will work hard towards my return to the ice and will learn from this frustrating setback." The Arizona Coyotes subsequently announced their full support of both the NHL/NHLPA Performance Enhancing Substances Program and Tinordi. In the following 2016–17 season, upon serving his suspension Tinordi was placed on waivers by the Arizona Coyotes on October 21, 2016, and sent to the team's AHL affiliate Tucson Roadrunners the next day. He scored the first Roadrunners goal in their home debut on October 28. He played out the entirety of the season with the Roadrunners, appearing in 64 games for 11 points. On July 1, 2017, Tinordi signed a one-year, two-way contract with the reigning Stanley Cup champions, the Pittsburgh Penguins. Tinordi was assigned by Pittsburgh to the Wilkes-Barre/Scranton Penguins for the duration of the 2017–18 season. As a key presence on the blueline, Tinordi established new professional highs with 5 goals and 21 points in 62 games. Tinordi left the Penguins in the off-season as a free agent to sign a one-year, two-way contract with the Nashville Predators on July 1, 2018. Prior to the start of the 2018-19 season, Tinordi was named captain of the Predators' American League affiliate, the Milwaukee Admirals. He spent the entirety of the season with the Admirals, recording eight goals and 22 points in 75 games. On May 29, 2019, the Predators re-signed Tinordi to a two-year, two-way contract extension. On January 29, 2020, Tinordi recorded his first career NHL goal against the Washington Capitals.
His father, Mark, was a defenseman who played for four NHL teams, and was the captain of the Minnesota North Stars when they moved to Dallas to become the Dallas Stars.
