While playing scholastic sports at Ayer High School in Ayer, Massachusetts, Morris was an All-State in two sports. Morris was a four-year starter at Syracuse University. At Syracuse, Morris set all of the all-time rushing records rushing for 4,229 yards in his four seasons surpassing former greats such as Jim Brown, Larry Csonka and Floyd Little. An All-American choice by his senior year, he was selected to play in the Blue–Gray, East–West Shrine and Senior Bowl games before signing on with the New York Giants. Morris was also co-captain with Ike Bogosian, father of NHL player Zach Bogosian.