Boggs played two sports while attending Dalton High School. He played baseball for the Catamounts under the direction of Coach Manny Pontonio. Boggs was a pitcher and also a 3rd baseman who was recruited to be a dual-sport college star.
Boggs also played quarterback for Dalton High's football team. His senior year, Boggs led the Catamounts to a 13–2 record, and an appearance in the AAA State Championship Game. He passed for 2,224 yards and 18 touchdowns and added 684 yards and 12 touchdowns on the ground that season.
Boggs signed a baseball scholarship at the University of Georgia but after one season in which he saw limited playing time, he described himself as "burned out" and transferred to the University of Tennessee at Chattanooga where he was a walk-on quarterback for the Mocs' football team. After only one semester at UTC he transferred back to UGA and helped the Bulldogs reach the 2004 College World Series. While at Georgia, Boggs pitched for the Newport Gulls of the New England Collegiate Baseball League. He appeared in 8 total games, owning a 6–0 record, including a 0.91 regular season earned run average (ERA) and two wins in the playoffs. Drafted by the St. Louis Cardinals after his junior year, Boggs left Georgia to begin his professional career.
On June 6, 2008, Boggs was promoted to the Cardinals' major league club from the Triple-A Memphis Redbirds to replace Mike Parisi on the active roster. In 12 starts with the Redbirds in 2008 before his promotion, Boggs was 5–1 with a 3.28 ERA.
On June 10, 2008, Boggs got his first start going five innings, giving up only four hits and two runs, in picking up his first victory, over the Cincinnati Reds, 7–2 in Cincinnati.
Boggs broke out in 2012, having the best year of his career. He had a record of 4 wins and 1 loss with an ERA of 2.21. He also led the National League in holds with 34.
Boggs spent part of 2013 as the closer for St. Louis, but he was sent to the minor leagues in early May with an ERA of 12.66. He came back to the Cardinals after 18 days on May 20 and blew Michael Wacha's 2-1 lead in his debut on May 30. He was demoted a second time to AAA-Memphis the next day.
On July 9, 2013, Boggs was traded to the Colorado Rockies for an international signing bonus. In 9 games for the Rockies, Boggs posted a 3.12 despite shaky command. After the season, Boggs was non-tendered by Colorado, becoming a free agent.
On February 7, 2014, Boggs signed a one-year $1.1 million deal with the Chicago White Sox. He was released on March 23. He re-signed to a minor league deal on April 1. He was released again on July 1, 2014 after posting an ERA over 9 in 25 games.
On July 21, 2014, Boggs was signed to a minor league deal by the San Francisco Giants. Boggs appeared in just 10 games for the Grizzlies, inducing 7 walks in just 13 innings for Fresno. He was released after the season.
On January 5, 2015, the Boston Red Sox signed Boggs to a minor league contract.
On April 20, 2015 Boggs signed a minor league deal with the Atlanta Braves. He was released on June 7.
Boggs married his high school sweetheart LeLe Crutchfield in December 2010. His brother Matthew Boggs played baseball for Georgia Tech and was a part of the Yellow Jackets' 2002 CWS team. Mitchell Boggs is not related to Baseball Hall of Famer Wade Boggs.