Kaufman died in his Santa Margarita home Saturday night, Cal Poly San Luis Obispo officials announced Monday. An autopsy was scheduled for Wednesday.
"Mel was a tremendous football player, as well as a fine talent evaluator," Redskins owner Daniel Snyder said in a statement released by the team. "His work on the field as a player and as a coach, and as well as his commitment to so many charities, were testament to how much he loved the game and the fans who cheered for him. Our prayers go out to his family during this sad time."
A defensive team leader and team captain with the Redskins from 1981 to 1988, Kaufman was a starting linebacker in NFC title games in 1982, '83 and '87. He started 78 of 91 games after making the team as a rookie free agent in 1981.
Kaufman was limited to six starts in 1988, his last season, after a shoulder and neck injury. After retiring, he was a scouting supervisor for the Redskins through 1998.
Kaufman had been working as linebackers coach at Cal Poly since last spring, and he helped guide the Mustangs to an 8-3 record, a Great West Conference title and their second NCAA FCS playoff berth.
Kaufman played on the school's Division II national championship team in 1980 and was a member of its athletic hall of fame.
"It's a tragedy. He was a good man and a compassionate man," said former Cal Poly coach Rich Ellerson, who became Army's coach in December. "I pray that the stress of the coaching business wasn't a contributing factor. He was just a good guy, a passionate guy, a Mustang."
Kaufman had been out of football for about 10 years before he was hired 11 months ago at his alma mater. During that time, he worked at a family-owned moving and storage company in Los Angeles, as a mental health counselor and coached football, basketball and baseball at Masada High School in Gardena, Calif.
"We took a bit of a chance with him because he hadn't coached before at this level, but there were a lot of compelling things in his background as a player and scout, as well as who he was as a person," Ellerson said.
Kaufman and defensive back LeCharls McDaniel, who also played for the Mustangs' 1980 national championship team, both were signed by Redskins general manager Bobby Beathard as free agents after a workout at Cal Poly in 1981.
"He was very cerebral, didn't make very many mistakes and brought a lot of life to the team," Beathard said.
Funeral arrangements for Kaufman were pending.
Information from The Associated Press was included in this report