Hanspard attended Texas Tech University, where he played for the Texas Tech Red Raiders football team from 1994 to 1996. As freshman in 1994, he recorded 761 yards rushing on 173 carries. In the following season, he had 1,374 yards on 248 carries. In 1996, he accumulated 2,084 yards rushing (and a total of 2,276 all-purpose yards). He was one of two running backs to rush for 2,000 yards that year, the other being Troy Davis. However, Hanspard edged out Davis for the Walker Award in part because he played on a winning team. He was recognized as a unanimous first-team All-American, and finished sixth in the voting for the 1996 Heisman Trophy. He was only the third Red Raider to be named a unanimous All-American, after Mark Bounds in 1991 and Zach Thomas in 1995. He has since been joined by Michael Crabtree in 2007-08 and Jace Amaro in 2013.