Thagard resumed his academic studies in 1971 after a stint in the U.S. Marine Corps and received a doctor of medicine degree from the University of Texas Southwestern Medical School in 1977. Prior to his joining NASA, he was interning in the Department of Internal Medicine at the Medical University of South Carolina.

Thagard was selected as an astronaut candidate in 1978. His first mission into space was as a crew member on STS-7 in June 1983. During the mission, they deployed two satellites, deployed and retrieved the Shuttle Pallet satellite, and conducted a series of scientific investigations.
His second flight into spacee was on STS-51B, the Spacelab-3 science mission, in April/May 1985. His duties on the mission included deploying the NUSAT satellite, caring for animals in the Research Animal Holding Facility and operating a variety of other experiments.
Thagard went to space for a third time in May 1989 on the STS-30 mission. The mission's highlight was the deployment of the Magellan probe, the first U.S. planetary mission since 1978, which was going to pay a visit to Venus.
His fourth flight, in January 1992, was on STS-42. The flight, called the International Microgravity Laboratory-1 mission, featured 55 experiments from 11 countries, which studied the effects of microgravity on material processing and life sciences.

Thagard became the first American to ride on board a Russian launch vehicle when he was launched to the Russian space station Mir on March 14, 1995.

At the end of his three-month mission on Mir, he held the American record for the most time spent on orbit. His record was broken by Shannon Lucid in August 1996.