Kaufman was born in Kansas City, Missouri and grew up in Lompoc, California, 55 miles west-northwest of Santa Barbara.
As a senior in 1990, at 5-foot-9, 170 pounds, with 4.3-second speed in the 40-yard dash,[2] he was named the Cal Hi Sports California High School Football Player of the Year.
In 1991, as a true freshman at Washington, Kaufman returned kicks for the Huskies during the year the team won the national championship.
In September 1992, Sports Illustrated reported Kaufman to have recently been timed at 4.22 seconds in the 40-yard dash, with teammate Jason Shelley commenting, "Nobody runs with Napoleon.
In 1994, he was a second-team All-American, finished ninth in Heisman Trophy voting (receiving three first-place ballots),[12] and is a member of the University of Washington Hall of Fame.
Kaufman rushed for 490 yards as a rookie backing up Harvey Williams; also during his debut season, he scored on an 84-yard kickoff return for a touchdown in a win over the Indianapolis Colts.
Kaufman broke the record of 221, set by Bo Jackson in his famous Monday Night Football performance against the Seattle Seahawks on November 30, 1987.
[16] During the latter part of his playing career, Kaufman was the Raiders' chaplain, and baptized several teammates in the whirlpool at the team's practice facility.