Though he never took a snap in high school, Texas coach Darrell Royal envisioned Saxton as a quarterback, and so during his freshman and sophomore years that was the position he played.

That season, he set the school and Southwest Conference record for yards per carry, became Texas' first consensus All-American running back, and finished third in Heisman voting behind Syracuse's Ernie Davis and Ohio State's Bob Ferguson.

After beating everyone but Oklahoma by at least 3 touchdowns and with only two very beatable teams left on the schedule, they seemed to be a lock to finish the season ranked #1.

During the 1963 off season, the Texans moved to Kansas City to become the Chiefs and Saxton declined to go with them; he only wanted to play in Texas to stay close to his business interests.

He died of dementia on May 28, 2014, and was buried on the shores of Red Lake near the town of Fairfield, Texas.