Born in 1904 in Warren, Rhode Island, Morrissey attended La Salle Academy in Providence. After high school, he enrolled at Holy Cross College in Worcester, Massachusetts, playing varsity baseball for three years (1924 through 1926). He thrived under the tutelage of Jack Berry, a New England legend who coached at Holy Cross from 1921 through 1961. Berry's program produced several fine ballplayers, including Gene Desautels, who caught for the Tigers, Red Sox, Athletics, and Indians from 1931 through 1946. Dividing his time between the outfield and middle infield, Morrissey was a member of three Holy Cross championship clubs when the school competed in the old Eastern Intercollegiate Baseball League. 

In 1927, his first year in minor league ball, Morrissey played for both Hartford and Buffalo of the Class B Eastern League (statistics are not available) as well as 26 games for Scottdale of the Class C Middle Atlantic League (98 at-bats, 21 runs, 40 hits, 4 home runs, and 2 stolen bases). He spent the next two years playing for Clarksburg of the M.A.L.. Although the Generals struggled both seasons, Morrissey showed some promise, batting .319 in 84 games during the 1928 season. The next year he boosted his batting average 35 points to .354. In 114 games and 449 plate appearances, he scored 87 runs, clobbered 12 home runs, and stole 38 bases. 

After posting impressive numbers in the Middle Atlantic League, he earned a promotion to the Class B Three Eye. For Bob Coleman's Evansville club, Morrissey appeared in 135 games, hitting .321 in 530 at-bats. He scored 92 runs, stole a career-high 39 bases, and led Three-I League second basemen with 318 putouts and 72 doubles plays. The Hubs won 79 and lost 55 to capture the league's split-season pennant. Coleman's talent-rich roster included future big leaguers Tommy Bridges, brothers Gee and Hub Walker, and Jo-Jo White. All four would enjoy more productive Major League careers than the hard-luck Morrissey. 

After his one season in the Illinois-Indiana-Iowa League, Morrissey spent 1931 playing for St. Paul of the American Association. In 167 games in the competitive A.A., he batted .331 with 123 runs, 223 hits, and 22 home runs (compared to only 4 roundtrippers in Three Eye play). The Saints finished atop the standings with 104 wins and 63 losses. In the 1933 edition of Who's Who in Major League Base Ball , Morrissey paid credit to Coleman and Bob Connery, part-owner of the Saints, for shepherding his career. 

In 1932, the 28-year-old earned a roster spot with the Cincinnati Reds. In 89 games (45 at short, 42 at second, and 12 at third) he struggled at the plate, hitting a weak .242 in 269 at-bats. The following year he appeared in 148 games for the last-place Reds (58-94), appearing at second base (88 games) short (63) and third (15). He struggled with a finger injury, and his batting average dropped 12 points to .230. The following season there were no big league openings available for a light-hitting, 30-year-old utility infielder. 

Where Morrissey spent the 1934 or 1935 seasons is unknown, though by 1936 he resurfaced in the Majors, appearing in 17 games for the Chicago White Sox. His season was cut short due to a broken cheekbone. He then toiled in the minors for several years before suffering a career-ending Achilles tendon injury. Jo Morrissey died on May 2, 1950 in Worcester. He was 46-years old.