Grimm was drafted by the Texas Rangers in the fifth round of the 2010 Major League Baseball draft out of the University of Georgia. Grimm made his MLB debut on June 16, 2012, against the Houston Astros. He won his debut, pitching six innings, striking out seven, walking none, and throwing 88 pitches for 56 strikes. Grimm was the first pitcher to have seven strikeouts and no walks in a debut since Stephen Strasburg's debut on June 8, 2010. On May 2, 2013, Grimm was named American League Rookie of the Month for April. During April, Grimm held a 2–0 record with a 1.59 ERA in 3 starts, striking out 15 and holding opponents to a.239 batting average in 17.0 innings. In the first half of the 2013 season, Grimm went into the All-Star Break with a 7–7 record and a 6.37 ERA. His final three Rangers appearances saw him go 0-2 and pitch 11.1 innings, giving up 23 hits, 6 walks, and 15 runs.
Chicago Cubs
The Rangers traded Grimm to the Chicago Cubs on July 22, 2013, with Mike Olt, C. J. Edwards, and Neil Ramirez, in exchange for Matt Garza. He was optioned to the Triple-A Iowa Cubs on July 23 and lost his first start for Iowa, giving up 7 earned runs in two innings including six straight hits to start the second inning. When major league rosters expanded in September, Grimm was recalled to the Cubs. Grimm finished the season in the Cubs' bullpen, working 9 innings and posting a 2.00 ERA. Going into 2014 spring training, it was announced that Grimm would move to the Cubs' bullpen due to the considerable depth within the Cubs' starting rotation. At the end of spring training, Grimm made the Cubs' opening-day roster as a relief pitcher. On August 29, 2014, Grimm became the 68th pitcher in Major League history to strike out four batters in a single inning. Grimm finished the 2014 season with a 5–2 record, a 3.78 ERA and 70 strikeouts over 69 innings pitched, working primarily as a middle reliever. The following season he had a career low ERA of 1.99 in 62 games. In 2016, he worked 68 games with a 4.10 ERA in. He helped the Cubs to their first World Series championship since 1908 by pitching in three of the seven games. In his final season with the team in 2017, he had a 5.53 ERA in 50 games. On March 15, 2018, the Cubs announced that Grimm was released from the organization.
Grimm was signed to a one-year deal with the Kansas City Royals on March 18, 2018. He was placed on the disabled list on June 27 with a back injury, his second stint on the disabled list in the first half of the season. On July 7, The Royals requested release waivers on Grimm.
Seattle Mariners
On July 19, 2018, Grimm signed a minor league deal with the Seattle Mariners. He was promoted to the major leagues when rosters expanded on September 1, 2018.
Grimm signed a minor league contract with the Cleveland Indians on January 3, 2019. The deal included an invitation to the Indians' 2019 major league spring training camp. Grimm opted out of his contract on March 22, 2019 after being informed he would not make the opening day major league roster.
On July 17, 2019, Grimm, was traded to the Cincinnati Reds. He became a free agent following the 2019 season.
Milwaukee Brewers
On December 4, 2019, Grimm signed a minor league contract with the Milwaukee Brewers.
Personal life
Grimm married longtime girlfriend Gina Nuccio, a former All-American gymnast at the University of Georgia, on January 30, 2016. Their son Austin was born in 2018.