Schwantz is a graduate of William Fremd High School in Palatine, Illinois, where he was a two-way player in football, receiving All-state and All-conference honors as a senior.
After accepting a scholarship from Purdue University, he started 5 games as a freshman and was a regular starter as a sophomore at outside linebacker. After finishing 1989 with 11 sacks, he broke his foot during the summer, sidelining him until the start of his junior season and contributing to him having an off year.
As a senior, he was switched to middle linebacker, registering 143 tackles (led the team), 102 solo (led the team), 12 tackles for losses, 2 sacks and one interception that he returned for a 66-yard touchdown. He was selected Big 10 defensive player of the week, for the 19 tackles he made against Northwestern University. He also was named to the Dean's List. At the time, he ended his college eligibility with 363 career tackles (sixth in school history), 18 career sacks (school record), 11 sacks in a season (school record) and 43 career tackles for loss (second in school history).
Schwantz was signed as an undrafted free agent by the Chicago Bears after the 1992 NFL draft. In his first two years, he appeared in one game as a rookie, spending most of his time on the practice squad.
On August 28, 1994, he was traded to the defending Super Bowl champions the Dallas Cowboys, in exchange for a sixth round draft choice (#201-Hayward Clay).
The Dallas Cowboys traded for Schwantz because they were thin at the linebacker position and because he knew their defensive system, having been coached by Dave Wannstedt, who was the team's defensive coordinator before moving on to the Chicago Bears. He was a part of the Super Bowl XXX winning team.
With the Cowboys he developed into an excellent special teams player, setting the franchise's single season record with 32 tackles on special teams (the NFL started keeping the stat in 1990), while being selected to the Pro Bowl in 1996.
He was declared a restricted free agent at the end of the season and although he was seen as a valuable player, the Cowboys had serious salary cap problems and could only tender him a qualifying offer at his original undrafted signing. The San Francisco 49ers signed him to a four-year offer sheet for $2 million that included a $600,000 signing bonus, that the Cowboys did not to match and did not receive any compensation.
In 1997, he registered 18 special teams tackles. He was cut on August 25, 1998, after the team decided to keep two younger linebackers (Anthony Peterson and Winfred Tubbs).
On August 29, 1998, he was signed by the Chicago Bears as a free agent, to improve the special teams units. He was released on August 18, 1999.
Schwantz played in 78 career games (no starts) and was credited with 39 defensive tackles, amounting to half a tackle per game.
On February 25, 2008, Schwantz declared his intention to run for mayor of the Village of Palatine, Illinois in the 2009 election.
On April 7, 2009, he secured 42% of the vote, defeating 20-year incumbent Rita Mullins, who ended up placing a distant third in a four-way mayoral race. Schwantz was sworn into office as Mayor of Palatine on May 4, 2009. He was re-elected to a second term as mayor in 2013, running unopposed.
Schwantz is a contributor to the WBBM 780AM Chicago Bears broadcast team along with former players Jay Hilgenberg and Tom Thayer.