Sweet began his top-level career in 2008, driving for Kasey Kahne Racing in midget cars and sprint cars in the USAC National Midget Series and World of Outlaws. He proved immediately competitive, winning prestigious events including the Knoxville Midget Nationals and scoring victories at Eldora Speedway in both sprint car and midget car competition. Sweet also pursued stock car racing in parallel, making starts in the ARCA Racing Series and NASCAR Camping World Truck Series from 2009. He drove partial Truck Series seasons for Stringer Motorsports and Turner Motorsports in 2010 and 2011, finishing 28th in series points in 2011.
In 2012, Sweet drove the No. 38 Nationwide Series Chevrolet sponsored by Great Clips and owned by Turner Motorsports in a limited schedule, competing in 18 races while Kasey Kahne shared the car for the remainder of the season. Sweet contended for the Nationwide Series Rookie of the Year award. He moved to JR Motorsports in 2013, driving the No. 5 Chevrolet Camaro on a part-time basis.
Sweet became a full-time World of Outlaws competitor with Kasey Kahne Racing's No. 49, sponsored by NAPA Auto Parts and Ollie's Bargain Outlet, beginning in 2014. He had recorded his first World of Outlaws win in 2012 at Clay County Speedway. In 2013 he won the prestigious Kings Royal at Eldora Speedway for his sole victory that season, finishing the year 18th in points. Sweet opened 2014 by winning the season opener at Volusia Speedway. He won the 2018 Knoxville Nationals, the first Nationals triumph for Kasey Kahne Racing, and finished second in the 2018 Kings Royal to Donny Schatz before returning in 2019 to win the Kings Royal for a second time.
Sweet's championship dominance began in 2019 when he claimed the title over Donny Schatz with 16 victories. He defended the championship in 2020 with eight wins, becoming the sixth driver in series history to win multiple World of Outlaws titles. He then won three further consecutive championships in 2021, 2022, and 2023. Across his World of Outlaws career Sweet accumulated 92 feature race victories from 895 starts.
Sweet and Kyle Larson co-founded High Limit Racing, a rival sprint car series, in 2022. Sweet left the World of Outlaws for High Limit in 2024, immediately winning the series' inaugural championship with ten victories. In 2025 he finished as runner-up with four wins, after which he announced his retirement from full-time racing.
Sweet's sister Katelyn is married to NASCAR driver Kyle Larson, his longtime business partner in SLC Promotions and High Limit Racing.