He played collegiately at the University of Northern Iowa and was selected by the Packers in the sixth round of the 1990 NFL draft.
In the first game of the 1991 season, Paup was involved in a tackle below the waist on quarterback Randall Cunningham of Philadelphia Eagles that saw contact on the knee for what was soon diagnosed as a torn ACL for the quarterback that sidelined him the rest of the season (Cunningham was quoted as curious about why his knee was hit like that when Paup was already down around the waist but did not wish to put a burden on him).
[3] Paup was utilized in four defensive positions during his Green Bay years, which would see him record 11 sacks in 1993 but somehow was not a Pro Bowl selection.
[9] On February 15, 1998, Paup signed a five-year contract worth $22 million with the Jacksonville Jaguars, making him the second highest-paid linebacker in the league next to Junior Seau.
[10] Troubles with being asked to drop into coverage and a decline in sacks (having just 7.5 in 31 games) led to his unhappiness in Jacksonville; he was released after the 1999 season ended.
On March 5, 2013, Paup resigned from Green Bay Southwest and began his first season as the defensive line coach at the University of Northern Iowa.