After sitting three seasons behind Mike Tomczak and Jim Karsatos, Tupa took over the starting quarterback job at Ohio State University in 1987, throwing for 2,252 yards, 15 touchdowns and 12 interceptions. He was selected as an All-American punter in the same season, as well as All-Big 10. Tupa was a four-time football letterman and was also selected to play in the 1988 Hula Bowl all-star game.
Tupa was drafted in the third round (68th overall) of the 1988 NFL Draft by the Phoenix Cardinals. During his rookie year, he was used exclusively as a quarterback, playing in two games and completing 4-of-5 passes for 49 yards. His second season with the team saw an expanded role. He started two games at quarterback, while registering six punts for 46.7 yards per punt. After spending the entire 1990 season as strictly a holder on kicks, he was the primary quarterback for the Cardinals the following year, playing in 11 games and throwing six touchdowns to 13 interceptions. He then joined the Indianapolis Colts in 1992, playing as a backup quarterback to Jack Trudeau and Jeff George.
That season also marked the last time Tupa was used regularly as a quarterback; since then he almost exclusively punted, with only emergency occasions or trick plays making use of his throwing skills. Tupa sat out the 1993 NFL season, having been cut by the Cleveland Browns right before the season. However, he was re-signed by the Browns the following year and stayed with them for two seasons as their starting punter. He joined the New England Patriots in 1996 and played for them for three years. In 1999, Tupa signed with the New York Jets. It was during this season that Tupa received his first invitation to the Pro Bowl. He also made his first pass attempt since 1996, and went 6-of-11 for 165 yards and two touchdowns. 2002 saw Tupa sign with the Tampa Bay Buccaneers, where he was their punter on their road to Super Bowl XXXVII, where they defeated the Oakland Raiders. Before the start of the 2004 NFL season, Tupa signed with the Washington Redskins. In 2004, he was named as a Pro Bowl second alternate. He spent 2005 on the injured reserve list, and did not appear in a game.
Tupa announced his retirement from pro-football in the spring of 2006. In February 2006, he was appointed as the recreation director of Brecksville, Ohio.
Tupa scored the first two-point conversion in NFL history, running in a faked extra point attempt for the Browns in a game against the Cincinnati Bengals in the first week of the 1994 season. He scored a total of three such conversions that season, earning him the nickname "Two Point Tupa."
The final pass of Tupa's career was thrown in overtime of the 2002 season-opener against the New Orleans Saints during a punt attempt from the Buccaneers' five-yard line. Pressure from a Saints defender forced Tupa to abort the punt attempt and throw a desperation pass with his non-throwing arm which was intercepted by a Saints defender and returned for a touchdown, ending the game.