The Phillies selected Stassi in the 33rd round of the 2011 MLB Draft out of University of Nevada, Reno. Stassi debuted with the Williamsport Crosscutters in 2011, playing for them in parts of two seasons before joining the Lakewood BlueClaws, Clearwater Threshers and Reading Fightin Phils. His breakout season came with the Class AA Fightin Phils in 2015, when he posted a.300/.394/.470 with 15 home runs and 90 RBI in 133 games, helping lead Reading to first place in the Eastern League Division standings while earning an All-Star berth. Besides, Stassi led the league in RBI and doubles, ending second in total bases and walks, third in on OBP and runs scored, fifth in hits, and sixth in home runs. In addition to his offensive contributions, Stassi led Eastern League first baseman with a.995 fielding percentage, making five errors in 112 games. At the end of the season, he was selected as the winner of the 2015 Eastern League Most Valuable Player Award. In 2016, playing for the Class AAA Lehigh Valley IronPigs in the International League, he hit.267/.369/.437. Stassi made the Phillies' Opening Day roster in 2017. He made his major league debut on Opening Day. He was designated for assignment on August 31, 2017, to make room for newly-acquired Juan Nicasio on the 40-man roster. Stassi elected free agency on November 6, 2017.
On August 10, 2018, Stassi's contract was purchased by the San Francisco Giants. Following the 2018 season, he re-signed to a minor league deal on November 9. He became a free agent following the 2019 season.
On February 23, 2020, Stassi signed a minor league deal with the Oakland Athletics. Stassi was released by the A’s in March prior to the beginning of the season.
Long Island Ducks
On April 10, 2020, Stassi signed with the Long Island Ducks of the Atlantic League of Professional Baseball.
Personal life
Stassi's father, grandfather, and great-grandfather played as catchers in the minor leagues. His younger brother, Max Stassi, is a catcher who debuted with the Houston Astros in 2013. Brock and Max Stassi hold an annual charity event that began in 2009 in their hometown of Yuba City, California; the money collected goes to 12 food banks within a 50-mile radius of Yuba City and Hands of Hope, a charity that offers support to homeless children and their families. The event consists of a home run derby between the brothers at the Yuba City High School field. In 2014, the event was expanded to include a home run derby with one player from each of eight local high schools, taking donations based on the number of homers hit, as well as accepting flat-rate donations.