Born to Milan and Ljubica Šoškoćanin on 24 June 1958, Vukašin had two brothers, Radovan and Dušan. He became a member of the Serb Democratic Party in 1990. He was a veterinary technician in Vukovar. Šoškoćanin was president of the Borovo commune and commander of the Borovo Selo Territorial Defense Force during the Croatian War, most notably during the Battle of Borovo Selo.