Jeffcoat grew up in Matawan, New Jersey, and played high school football at Matawan Regional High School, where he earned All-American football honors while also lettering in wrestling; the school retired his jersey. He was a three-year starter at Arizona State University from 1980 to 1982. In 1981, he earned honorable mention All-Pac-10 honors. In 1982, he became the catalyst of the Sun Devils' No. 1 ranked defense. He collected 95 tackles, four sacks, four pass deflections, and forced two fumbles during his senior season, where he earned All-Pac-10, honorable-mention to the All-American Associated Press and Sporting News teams. He played in the East–West Shrine Game and in the Senior Bowl. On October 22, 1994, he was inducted into the Arizona State Hall of Fame, as arguably one of the greatest defensive linemen to wear a Sun Devil uniform, finishing with 20 career sacks. He also was inducted into the Arizona State Football Ring of Honor and the Fiesta Bowl Hall of Fame, after dominating a 1983 Fiesta Bowl victory, earning defensive player of the game in a 32–21 win over University of Oklahoma.
He was selected in the first round of the 1983 NFL Draft by the Dallas Cowboys. He was also selected by the Arizona Wranglers in the 1983 USFL Territorial Draft. He was a backup defensive end as a rookie. In 1984, he replaced Harvey Martin at the right defensive end position, registering 82 tackles to go along with 11.5 sacks, ranking second on the team and in the top 15 among sack league leaders. In 1985, he was second on the team with 12 sacks and in the top ten among league leaders. His most memorable game was against the Washington Redskins on November 10, 1985, when he tallied 11 tackles and sacked quarterbackJoe Theismann a franchise record 5 times, tying Bob Lilly’s 19-year-old mark. Against the New York Giants, he intercepted a Phil Simms pass that was batted down by Ed "Too Tall" Jones and returned it 65 yards for a touchdown, making a critical play in a win that helped clinched the NFC East title. In 1986, he led the team with a career-high 14 sacks. Jeffcoat maintained a high level of play throughthe Cowboys difficult years of the late '80s. His best season came in 1989, when he finished with a career-high 100 tackles, a career-high 42 quarterback pressures, 11.5 sacks and a career-high three fumble recoveries. During the 1992 season his role was reduced to a situational pass-rusher, after Tony Tolbert took over the left defensive end position and the team traded for Charles Haley to make him the right defensive end. Even with fewer opportunities, he managed to lead the team with 10.5 sacks and six tackles for loss, during the team's drive towards winning Super Bowl XXVII. His repertoire of pass rushing moves and effort, allowed him to remain an effective player through the 1994 season, while playing mostly on passing situations. Jeffcoat left via free agency in 1995, after playing 12 seasons and never missing a game with the Cowboys. He finished with 698 tackles, 94.5 sacks and 149 quarterback pressures. He also accomplished five seasons with 70 or more tackles and five seasons with 10 or more sacks, leaving as the franchise official career sack leader.
Buffalo Bills
On February 22, 1995, he was signed as a free agent by the Buffalo Bills. He had a streak of 224 consecutive games played, before being sidelined on September 21 and eventually being placed on the injured reserve list on December 12, 1997. Jeffcoat retired after playing 15 seasons, with 102.5 sacks, 745 tackles, 194 quarterback pressures, 2 interceptions, 11 fumble recoveries and 2 touchdowns. At the time he ranked among the NFL's top-15 career leaders in sacks and his 227 games, placed him among the top 30 players in NFL history in games played. He was nominated for the Pro Football Hall of Fame Class of 2008 although he was never selected to a Pro Bowl.
Coaching career
After his retirement in 1997, he spent seven seasons as the Cowboys' defensive ends assistant coach. Jeffcoat spent his last five seasons in the organization as the defensive ends coach after two years as the club's assistant defensive line coach. On January 28, 2008, Jeffcoat was hired to join Kevin Sumlin's staff at the University of Houston as defensive line coach. Prior to arriving in Houston, Jeffcoat was in private business in the Dallas area for two years. From 2011 to 2012, Jeffcoat coached the San Jose State defensive line. In January 2013, he joined the University of Colorado Buffaloes as defensive line coach under recently hired head coach Mike MacIntyre. In November 2018, Jeffcoat was hired by Steve Spurrier as defensive line coach for the Orlando Apollos of the Alliance of American Football. In June 2019, Jeffcoat was hired by Bob Stoops as defensive line coach for the Dallas Renegades of the new XFL.
Personal life
Jeffcoat and his wife, Tammy, live just outside the suburb of Plano, Texas, with their four children: twins Jackson and Jacqueline, Jaren, and Jasmine. Jacqueline was a top 2010 class basketball center recruit for the University of Oklahoma, while Jackson played in the NFL for the Washington Redskins. He currently owns an Allstate insurance agency.