Initially noted for his diminutive stature — 5' 7", Morris was a key member of the Giants team that won Super Bowl XXI in 1987.

As a rookie with the Giants in 1982, Morris scored a touchdown on his very first rushing attempt; a prelude of what was to come for the powerful running back.

In the Giants' march to the Lombardi Trophy, Morris rushed for 313 yards in three playoff games including a 159-yard, two touchdown performance against the San Francisco 49ers.

As of 2017[update]'s NFL off-season, Joe Morris held at least 19 Giants franchise records, most related to his prolific post-season career with the club.

He was also a part owner of the New Jersey Red Dogs of the Arena Football League, along with fellow ex-Giants Carl Banks and Harry Carson.