Kaufman was selected with the 18th pick in the 1st round of the 1995 NFL Draft by the Oakland Raiders, where he remained for the entirety of his 6-year NFL career, amassing 4,792 yards rushing on 4.90 yards per carry. Kaufman scored a touchdown in his first NFL game against the San Diego Chargers. Kaufman rushed for 490 yards as a rookie backing up Harvey Williams. As the Raiders' primary running back in 1997 and 1998, he rushed for 1,294 and 921 yards, respectively, and had 65 total receptions during those two seasons. Kaufman split playing time with Tyrone Wheatley in the latter part of his career.