Armstead attended David W. Carter High School in Dallas, Texas, where he was coached by Freddie James. Armstead was part of a highly talented team that featured four other future NFL players — Clifton Abraham, Joe Burch, Le'Shai Maston, Darius Smith — and won the 1988 5A state championship (stripped by UIL in 1991), defeating Permian High School in the state semi-final game, which was portrayed as the state championship game in the 2004 film Friday Night Lights and 2017 30 for 30 What Carter Lost. The title was later forfeited due to eligibility infringements.
Armstead was considered the top high school football talent in Texas as well as nationwide by recruiting analysts. He had been an All-American since his sophomore year, and at that time was the only player to be selected as an All-American three years in high school.
Fellow D-I recruits Derric Evans and Gary Edwards asked Armstead to join them and others in a series of robberies of video stores and fast-food restaurants, but he refused. In September 1989, Evans and Edwards were sentenced to 20 years and 16 years, respectively, in prison.
Recruited by Jimmy Johnson, Armstead chose to attend the University of Miami. However, weeks later, Johnson left Miami to take over as the head coach of the Dallas Cowboys. After initial reports that Armstead might seek to be released from his commitment to Miami, since the coach who recruited him to play there had departed, Armstead chose to honor his commitment after Dennis Erickson was named head coach.
A college standout on 2 of Miami's 5 national championship teams (1989, 1991), Armstead's pro prospects were diminished after he tore his anterior cruciate ligament his sophomore season. As a result, he was not drafted until the eighth round of the 1993 NFL Draft, when he was selected by the New York Giants.
Armstead was interviewed about his time at the University of Miami for the documentary The U, which premiered December 12, 2009 on ESPN.
Armstead was a five-time Pro Bowler, elected between 1997 and 2001. Armstead had 752 career tackles with forty sacks and 12 interceptions for 175 yards.
Following a nine-year career with the Giants, he was signed to a three-year, $4.5 million deal by the Washington Redskins, where he played for two additional seasons.
He signed with the Carolina Panthers for the 2004 season, but he retired that year following a pre-season injury.
On June 13, 2007, Armstead signed a one-day contract with the New York Giants to officially retire a New York Giant.
On September 8, 2008, Armstead was hired by the Giants as a "special assistant/consultant". His responsibilities include special projects, defensive assignments, player development and free agent recruiting.
In February 2008, Armstead was featured as one of the pros on Pros vs Joes on Spike TV.