Iosif Moshiashvili was born in 1896 to a family of Georgian Jews. In the 1930s he worked as a physician in Tbilisi, the capital of Georgia. In September 1943 he was drafted into the Red Army as a military doctor and served as the chief of the X-ray department of Homefront Hospital #1436, attached to the 1st Ukrainian Front. In April 1945, Captain of the Medical Service Iosif Moshiashvili was awarded the Order of the Patriotic War, 2nd Class. His citation for the military award stated:
"Comrade Moshiashvili is the chief of an X-ray department, a physician with 15-years experience …. Despite the danger of his profession, he works 12-15 hours a day. Although he came down with dermatitis as a result of overwork, he continued to fulfill his duties. … He carried out more than 4,000 X-ray examinations, which involved 100 percent of the wounded [brought to him]. For his selfless work and his sensitive and responsive attitude to patients he deserves the state award of the Order of the Patriotic War, 2nd Class."
After the war, Iosif Moshiashvili worked at the Ministry of Health of the Georgian Soviet Socialist Republic. In January 1953, at the beginning of the "Doctors' Plot" affair, part of Stalin's anti-Jewish campaign, Moshiashvili was arrested and sentenced to a 25-year term in the Gulag camps. After Stalin's death and the ensuing rehabilitation of the arrested physicians, Moshiashvili was released from prison camp in May 1953.