Punch grew up in Newton, North Carolina, where he developed a taste for broadcasting through his high school's local radio program on station WNNC. He walked on to the North Carolina State University football team as a backup quarterback under coach Lou Holtz and graduated magna cum laude in 1975 with a degree in zoology. He earned his medical degree from Wake Forest University School of Medicine in 1979, funding both his undergraduate and medical education through prize money won racing at short tracks in North Carolina. Before his broadcasting career overlapped with medicine, Punch worked as an emergency medicine physician, initially at Halifax Medical Center in Daytona Beach, Florida in 1982 and later as director of emergency medicine at Bunnell Community Hospital in Palm Coast, Florida.
Punch began radio broadcasting for the Motor Racing Network in 1980. In 1984 he joined ESPN as a pit reporter for NASCAR races, also moonlighting at TBS and SETN in the same role. During the 1984 Atlanta Journal 500 he was the first to report on the eventually fatal injuries to driver Terry Schoonover.
He covered the Indianapolis 500 from pit lane for ESPN from 1989 to 2006 and again from 2010 to 2018, and served as the lead play-by-play voice for the network's Craftsman Truck Series coverage until ESPN lost that contract to Speed Channel after the 2002 season. In October 2006 he was named the lead lap-by-lap commentator for ESPN's Sprint Cup Series and Nationwide Series coverage beginning with the 2007 season, working alongside Rusty Wallace and Andy Petree. Dale Jarrett joined the team in 2008. ESPN replaced Punch with Marty Reid for 2010 and moved him back to pit road, where he remained until the network lost NASCAR broadcasting rights after 2014. He also called play-by-play for college basketball and football and served as a sideline reporter for college football during his tenure.
After ESPN's NASCAR rights expired in 2015, Punch returned to college football sideline work. He was among 100 employees let go by ESPN on April 26, 2017, following thirty years with the network, though he continued in the pit lane for IndyCar through 2018 before NBC Sports acquired those rights. He made additional appearances for ESPN in college football in 2019 and 2020.
Punch's dual background as a physician made him a distinctive presence in the NASCAR paddock. In 1988, at Bristol Motor Speedway, Rusty Wallace's front-stretch crash left the driver unconscious, and Punch — already on pit road — was the first person on the scene. He revived Wallace, who was able to start the following night's race with only minor injuries. At the same event Punch also assisted after Don Marmor's career-ending crash at Atlanta Motor Speedway, and is credited with helping save Marmor's life.
In 1989 at the Motorcraft Quality Parts 500, Punch was stationed at Richard Petty's pit stall when a fire broke out injuring two crew members, whom he treated on the spot. The incident prompted ESPN to mandate fire-proof suits for all of its pit reporters. Punch also aided injured pit crew members in several races during the 1990s, and on one occasion at a Nashville Superspeedway media luncheon he stepped away from the podium to help revive a young intern who had fainted.
After his ESPN tenure, Punch continued to work as a Principal Investigator for clinical research company Alliance for Multispecialty Research in Knoxville, Tennessee, where he and his wife Joanie have lived since 2000. He also does local radio spots in Knoxville. They have a son Logan and a daughter Jessica.