 After serving at the LSU Service Charity Hospital in New Orleans and a year of neurosurgery at the University of Texas Medical Branch (UTMB) in Galveston, Texas, Griffith began preparing to become a radiation oncologist, one who specializes in using radiation to cure cancer, training in radiation oncology through a combined program between UTMB and M.D.Anderson Cancer Center in Houston.He served as a Medical Corps captain in the U.S. Army Reserve from 1970 to 1973, while continuing his medical training at the LSU Service Charity Hospital in New Orleans.