Grossman grew up in Cypress, Texas, where he played four seasons of varsity baseball at Cy-Fair High School between 2005 and 2008. He was a first-team all-district selection as a freshman. In his junior season, the team won the 5A state baseball championship. "He was fun to coach because he worked very hard at practice and looked like he was having the time of his life playing the game. We knew early on as a coaching staff that he was a special player," said a former high school coach, John Pope.
Professional career
Minors
Considered a possible first round pick, Grossman fell in the 2008 Major League Baseball Draft due to his commitment to attend the University of Texas. However, the Pirates selected Grossman in the sixth round of the draft and signed him for an above slot $1 million signing bonus. In 2010, Grossman played for the Bradenton Marauders of the Class A-AdvancedFlorida State League. In 2011, again playing for the Marauders, Grossman became the first minor league player since Nick Swisher in 2004 to score 100 runs and walk 100 times in a season; he also became the first player in the FSL to do so since 1998. He was named Minor League Player of the Year for the Pittsburgh organization. Kevin Goldstein of Baseball Prospectus ranked Grossman as the 76th best prospect in baseball before the 2012 season. The Pirates invited Grossman to spring training in 2012. On July 24, 2012, the Pirates traded him to the Houston Astros along with Rudy Owens and Colton Cain for Wandy Rodríguez. Between Pittsburgh's Class AA affiliate, the Altoona Curve of the Eastern League, and Houston's Class AA team, the Corpus Christi Hooks of the Texas League, Grossman hit.266 with 10 home runs in 131 games.
Houston Astros
The Astros promoted Grossman to the major leagues on April 24, 2013, he batted leadoff in his debut. He split time that year between the Oklahoma City Redhawks of the Class AAAPacific Coast League and the Astros. At one point, Grossman hit safely in 13 consecutive games, a team high that year. Grossman played in 103 games for the Astros in 2014, hitting for a.233 batting average, six home runs and 37 runs batted in. After spending much of the 2015 season in the minors, he was released by the Astros after the 2015 season.
On December 11, Grossman signed a minor league contract with the Cleveland Indians, receiving a non-roster invitation to spring training. He opted out of his contract on May 16, 2016 and signed with the Minnesota Twins. The Twins promoted him to the major leagues on May 19, and he hit a home run in his first game with the Twins on May 20. He split time among first base, left field and DH. He appeared in 99 games for the Twins, setting career highs in home runs, average, walks and runs scored. In 2017, he established himself as a regular in the Twins’ lineup, playing in a career-high 119 games despite missing a few weeks with a thumb fracture, hitting.246 with 9 HR and 45 RBI. In 2018, Grossman began the season as the Twins' designated hitter. He played in a career-high 129 games, hitting.273 with 5 home runs and 48 RBIs. On November 30, 2018, the Twins non-tendered him and he became a free agent.
Oakland Athletics
On February 15, 2019, Grossman signed a one-year deal with the Oakland Athletics. Grossman did not perform as he did the previous season, as he hit just.240 with 6 home runs and 38 RBI in 138 games.