Skočić, who was a midfielder, played professional club football in Croatia for the football club Rijeka, in Spain for the football clubs Las Palmas and Compostela, and in the UAE for Ittihad Kalba'. He was the first player from the Croatian football league who went abroad to play professionally.
After his playing career, Skočić went on to complete the Football Academy at the Croatian Football Academy and the Coach Education and Training Department at the Faculty of Kinesiology, University of Zagreb, receiving a UEFA-PRO Coach diploma and a Professional Bachelor of the Coaching Profession.
In 2007, he became the head coach of the Slovenian club Interblock Ljubljana. While the club was in a difficult situation on the league scale. Only two years after the club was founded and under the management of Skočić, the club achieved outstanding results in the Slovenian PrvaLiga. Not only did they manage to stay in the first league, but they also won two trophies in the 2007–08 season, the Slovenian Cup and a Super Cup.
In the 2009–10 season, Skočić took over the management of the Al Arabi club in Kuwait. Under his leadership as head coach, Al Arabi played in two finals, the Crown Prince Cup and the Federation Cup. Also under Skočić, Al Arabi played in the AFC Cup quarterfinals. Following Kuwait, in the 2010–11 season, Skočić was engaged by the Al Nassr football club from Riyadh, Saudi Arabia, one of the most prominent football clubs in the Arab world. Under Skočić, Al Nassr qualified for the third round of the AFC Champions League, after having played a successful season of competitions within the group.
In the 2011–12 season, Skocic again took over the management of his home club Rijeka. Skocic left the club in mutual agreement with the management. On 26 May 2013, Skocic was announced as the head coach of Malavan for the upcoming season. He signed a two years contract with the club. He led the club to the 7th place, their best league finish since 2005.