Joseph O'Connor was educated in Cabra, Dublin and later at Blackrock College where he played rugby. He later earned his dental degree from the Royal College of Surgeons in Ireland and practiced dentistry in Dublin until he joined the British Army in 1928, serving in the dental corps, for which he would later be awarded an MBE. O'Connor was a reserve with the 1924 Irish Olympic water polo team, but played at the 1928 Olympics. His brother, Michael O'Connor, was also on both teams. Joseph later returned to Dublin, living there until his death. Joseph's uncle was Michael O'Connor (1876-1926) who won three Irish athletic titles at the Gaelic Athletic Association Championships: the 1899 shot put, 1900 28lb weight put; and the 1901 56-lb weight throw.