Tynan was born in Dublin, Ireland. His family home is in Johnstown, County Kilkenny, Ireland. He was born with phocomelia, causing both of his lower legs to be underdeveloped; his legs were unusually short (he is now 6-foot 4), his feet were splayed outward, and he had three toes on each foot. He was one of a set of twins; his twin brother Edmond died at 11 months old. At age 20, he had his legs amputated below the knee, after a back injury from a car accident; the injury to his back made it impossible for him to continue using prosthetic legs without the amputation. Within weeks of the accident, he was climbing stairs at his college dormitory on artificial legs. Within a year, Tynan was winning in international competitions in track and field athletics. He represented Ireland in the 1984 and 1988 Summer Paralympics, winning four golds, two silvers, and one bronze medal. Between 1981 and 1984, he won 18 gold medals from various competitions and set 14 world records.