Cornwell attended Canyon High School, where he practiced football, basketball and track (shot put).
He accepted a scholarship from the University of Southern California, where he contributed as a three-year starter with his blocking at the tight end position.
Cornwell was selected by the Dallas Cowboys in the third round (81st overall) of the 1984 NFL draft, with the team looking to improve the depth of the tight end position after the retirement of Billy Joe Dupree.
As a rookie, he missed 2 games with a back injury and was mainly used for blocking on short yardage situations.
Against the Houston Oilers with the score tied at 10, he caught a one-yard touchdown pass with 1:51 minutes remaining to seal the win.