Sauter comes from one of American short-track racing's most recognizable families. His father Jim Sauter built a career in NASCAR, and both brothers Tim and Johnny also raced professionally. Jay's nephew Travis Sauter (son of Tim) continued the family's racing tradition into the next generation. Before reaching NASCAR, Sauter honed his craft in the American Speed Association (ASA), a proving ground for Midwest-based stock car talent.
Sauter made his NASCAR debut in 1996 in the Craftsman Truck Series, joining the prominent Team SABCO organization in the No. 42 Chevrolet Silverado. He qualified 21st and finished eighth at Homestead-Miami Speedway, then earned a best finish of third at Bristol Motor Speedway across six additional races that season. His strong run at Bristol even drew an offer for a ride in one of SABCO's Cup Series teams, but Sauter declined. He closed out 1996 driving the No. 03 for Richard Childress Racing at Las Vegas.
In 1997, Sauter stepped into Childress' No. 3 GM Goodwrench truck, replacing Mike Skinner. The season was a breakthrough: he won his first career race at New Hampshire Motor Speedway, recorded fifteen top-ten finishes, and finished sixth in the final points standings. The following year brought further progress, with a second career win at Martinsville Speedway and a career-high fourth-place finish in the championship. In 1999, Sauter added two more victories — at Louisville and Texas — though his points standing dipped to fifth.
For 2000, Sauter moved up to the Busch Series, driving the No. 43 Chevrolet Monte Carlo for the Curb Agajanian Performance Group. He recorded eight top-ten finishes, placed seventeenth in championship points, and finished fourth in the Rookie of the Year standings. In 2001, driving for the same team, he won his first career Busch Series pole at Kentucky Speedway. A potential breakthrough win at Memphis unraveled with two laps remaining when Jeff Green made contact in turn three, allowing Randy LaJoie to take the victory. Sauter was released by the team shortly after and missed two races before landing a seat in the No. 25 U.S. Marine Corps Chevrolet fielded by Ed Rensi.
In 2002, Sauter returned to Richard Childress Racing, sharing the No. 21 Rockwell Automation Chevrolet with Jeff Green across thirteen starts, with a best finish of fourth at Nashville Superspeedway. He also made his Winston Cup Series debut that year, driving the No. 71 for Marcis Auto Racing at Texas and Talladega. He completed the Busch schedule with Angela's Motorsports at the season finale at Homestead.
From 2003 through 2004, Sauter ran limited Busch schedules for Henderson Bros. Racing, achieving a ninth-place finish at Nashville in 2003 and a thirteenth at Richmond in 2004. He also returned to the Craftsman Truck Series during 2004 for four starts with MRD Motorsports.
After a single Busch Series start in 2005, Sauter returned in 2006 with the newly formed Duesenberg & Leik Motorsports, qualifying for 33 of 35 races and recording a best finish of seventh at O'Reilly Raceway Park. When that team merged with Davis Motorsports, Sauter moved to Frank Cicci Racing in 2007 for a handful of races before the operation suspended activity.
Following the end of his national-series career, Sauter returned to his roots, competing in local short-track races in Wisconsin.
Across his Craftsman Truck Series career, Sauter won four races — New Hampshire (1997), Martinsville (1998), Louisville (1999), and Texas (1999) — establishing himself as a consistent competitor in NASCAR's truck division before transitioning to the Busch Series. His career reflects the path of many Midwestern short-track veterans who built success in NASCAR's supporting series without fully breaking through to the premier Cup level.