In an announcement released on Wednesday, the club said that Bišćan and Mandarić had failed "to find a solution for further work".
The 40-year-old former Dinamo Zagreb, Liverpool and Panathinaikos player have had a number of meetings in the recent days, assessing that the developments in the past season had shown that "cooperation in joint interest is simply no longer possible".
The dismissal comes despite Bišćan, who signed a two-year contract last June, leading the club to the double title this year, including the national championship that was snatched from the hands of the perennial champions Maribor in the last round.
"Regardless of everything, I want to stress that Igor Bišćan has completed his mission in the club in line with the goals. I wish him all the good and many successes in his future career," Mandarić said.
Bišćan thanked the owner and president of the club for the trust and all the staff and players who had "contributed to this season becoming a historic season for us".
Mandarić had criticised Bišćan on several occasions in the media, assessing that the play is too defensive, that the title should have been secured a few rounds earlier, and that the coach should have given more time to young Slovenian players.
As the dismissal was looming in the last few days, the fans of Olimpija Ljubljana expressed their dissatisfaction on Tuesday, saying on their Facebook profile that the "acts behind the scenes" had ruined the atmosphere created after the club won the double title.
"The rumours that the club is replacing the coach who has brought us the double title after 25 years, who the fans grew fond of and who in our opinion works hard, seem absurd to us," said the Green Dragons.
They also hinted that the number of fans showing up for the club's games might drop, noting for example that Bišćan's former club Dinamo Zagreb were the "perennial national champions, but the stands are shamefully empty".
"It seems that the picture will be no different here. Instead of the attendance growing, apathy will start creeping in soon as a reflection of the distrust in the club's management".
Bišćan had little coaching experience prior to Olimpija Ljubljana, having previously coached only NK Rudeš from Zagreb in the second Croatian league.
Olimpija added in the press release that it would reveal the name of the new head coach in the coming days. The name that has been floated the most in the media is Slaviša Stojanović, the former national team head coach.