As a child Aumont's first love was baseball. He played with different regional and provincial teams, while attending high school at École secondaire du Versant in Gatineau, Quebec. Aumont was 15 years old when his hometown Montreal Expos left for Washington, D.C. after the 2004 season, but still supported the team despite playing in a new location.
Professional career
Seattle Mariners
Aumont was drafted by the Seattle Mariners with the 11th overall pick of the 2007 Major League Baseball draft and signed a contract which included a $1.9 million signing bonus. Aumont appeared in 15 games in 2008 for the Seattle Mariners A level affiliate, the Wisconsin Timber Rattlers, posting a 2.75 ERA over 55 innings with 50 strikeouts versus 19 walks. He began the 2009 baseball season with the High Desert Mavericks, the Seattle Mariners Advanced A affiliate, where he was converted into a reliever. In 29 appearances he posted a 3.24 ERA with 12 saves as the closer, earning a promotion to the Double-AWest Tenn Diamond Jaxx in mid-July. He finished the 2009 season with a 2–6 record, 16 saves, 3.88 ERA, and 59 strikeouts in 51 innings pitched. In the offseason, Aumont played in the Arizona Fall League for the Peoria Javelinas, and posted a dismal 12.00 ERA in 10 appearances.
Philadelphia Phillies
On December 16, 2009, Aumont was traded to the Philadelphia Phillies along with Tyson Gillies and J. C. Ramírez for Cliff Lee. Aumont played the 2010 season with the Advanced-A Clearwater Threshers and Double-A Reading Phillies, posting a combined record of 3–11, a 5.68 ERA, and 115 strikeouts in a career-high 122 innings pitched, mostly as a starter. He was moved back to a relief role for the 2011 season and made 43 total appearances for Double-A Reading, as well as the Triple-ALehigh Valley IronPigs. Aumont began the 2012 season in the bullpen for Triple-A Lehigh Valley, posting a 3–1 record, 4.26 ERA, and 59 strikeouts in 44 innings pitched. On August 20, he was promoted to the majors for the first time. He made his MLB debut on August 23, pitching a scoreless inning against the Cincinnati Reds. Aumont finished the season in the Phillies bullpen, appearing in 18 games and posting a 3.68 ERA with 2 saves. After opening the 2013 season in the Phillies bullpen, Aumont was demoted to Triple-A on May 23. He made 22 total appearances at the major league level in 2013 as well as 32 appearances in the minors, and struggled with command, walking 51 batters in 55 combined innings. On June 1, 2014, Aumont was recalled by the Phillies; he pitched in his first game back on the roster and took the loss. Aumont appeared in just 5 games for the Phillies, posting an ERA of 19.06. During the 2015 season with Lehigh Valley, Aumont transitioned back to a starter for the first time since 2010. After posting solid numbers in Triple-A, Aumont was called up in June but struggled mightily with his control, walking 7 batters and serving up 2 home runs in just 4 innings. It was his lone start as the Phillies designated him for assignment afterwards. On June 24, Aumont declined his outright assignment and instead became a free agent.
On November 23, 2015, Aumont signed a minor league contract with the Chicago White Sox. Aumont pitched to a 12.27 ERA over 11 innings with the Triple-A Charlotte Knights, and announced his retirement on June 6, 2016.
On January 9, 2018, Aumont signed a minor league contract with the Detroit Tigers. He elected free agency on November 3, 2018.
Return to Ottawa
On January 10, 2019, Aumont signed with the Ottawa Champions of the Can-Am League for the 2019 season. On July 16, 2019, Aumont threw 18 strikeouts in a complete game victory over the Rockland Boulders, setting a Can-Am League record for strikeouts in a single game. He finished the season with the lowest ERA and fewest earned runs against among all Can-Am League starters, and was named the 2019 Pitcher of the Year. Aumont became a free agent after the Champions franchise elected to take a season off following the Can-Am League's merger with the Frontier League. On October 25, 2019, Aumont was drafted by the Québec Capitales in the Ottawa Champions dispersal draft.
Toronto Blue Jays (second stint)
On December 2, 2019, Aumont signed a minor league contract with the Toronto Blue Jays. On June 30, 2020, Aumont announced his retirement on CBC Radio.
Aumont was a "power" pitcher, with a hard fastball and sharp breaking ball. Standing and weighing, Aumont threw a fastball in the mid 90s, reaching the upper 90s on occasion, with late movement. His breaking pitch was a "power slurve" which moves more like a curveball and had been clocked in the high 70s to low 80s. He also threw a changeup on occasion. During the 2014 offseason, Aumont commented that he has "always idolized" Randy Johnson, who is tall: