Born in Sarajevo, SFR Yugoslavia, Mulalić started his career with hometown club Željezničar on 4 occasions with whom he has won 3 league titles, 2 cups and 3 supercups. He played 220 league games for Željezničar and 322 games in all competitions. In Bosnia and Herzegovina, he also played for TOŠK Tešanj. Mulalić also played in Germany for Uerdingen 05, Eintracht Frankfurt with whom he won the 2. Bundesliga, and Hamm. He finished his playing career in 2010 winning one of the three league titles throughout his career as club captain with Željezničar at the age of 35.
In September 2016, he was named the new manager of Montenegrin First League side Dečić. He made the biggest result in the club's history by finishing 5th in the league. After the end of the season, Mulalić decided to leave the club.
In June 2017, Mulalić came back to Bosnia and Herzegovina and became the new manager of Bosnian Premier League club Mladost Doboj Kakanj. After 4 league rounds Mladost were first on the league table. When the winter break started Mladost were 6th. In April 2018, about a month and a half before the end of the season, Mulalić left the club as it already secured safety from relegation. It was unsure why he left, but it was said that he left because the thought of the games being "rigged". When Mulalić left, Maldost were 7th in the league, while at the end they finished 8th.
Rudar Pljevlja
On 21 July 2018, Mulalić was named the manager of another Montenegrin First League club, Rudar Prijedor. On 24 December 2018, Mulalić, alongside some of the players left the club due to financial problems that it had over the past months. Both sides said that they were on good terms.
On 31 January 2019, Mulalić became the new manager of yet another Montenegrin club, Titograd. After only 2 months as Titograd manager, Mulalić resigned from the position after a loss against Zeta.
Return to Rudar Pljevlja
In July 2019, more than half a year after leaving the club, Mulalić came back to Montenegro and once again became the manager of Rudar Pljevlja. In his first game in his second mandate as the club's manager, Mulalić's Rudar Plevlja lost 2–0 away in a league match against Budućnost Podgorica on 5 August 2019. His first win m since his return to the position of manager of Rudar came on 14 August 2019, in a 0–1 away league win against Mulalić's former team Titograd.
