In college, Cora played for Vanderbilt University. In June 3, 1985 he was drafted by the San Diego Padres in the first round. As a member of the Beaumont Golden Gators Cora received national attention when on June 22, 1986 he was stabbed after a game in San Antonio, Texas. Cora, who was had been a first round draft pick, was waiting outside the team bus following the game against the San Antonio Missions at V.J. Keefe Stadium when two men called his name and then assaulted him. He was stabbed once in the stomach and once in the arm. Cora was quickly rushed to the hospital and later made a full recovery after spending six weeks on the disabled list. A man named Jose Puente, 29, was caught at the scene and was later charged with attempted murder. No motive was ever given for the crime.