Kaufman graduated from the University of Arkansas at Monticello, playing at the Linebacker position for the Boll Weevils. During his playing career, he was named an All-American twice. After graduating in 1980, he served as a graduate assistant for Delta State University. In 1983, he received his first full-time coaching position as outside linebackers coach for Northwestern State. He held the position until 1987, when he was promoted to defensive coordinator in addition to his linebacker coaching duties.