Muller did not make the playoffs in three years behind the bench.
The moves are the first made by new general manager Ron Francis, who last week took over for Jim Rutherford.
"We thank Kirk, John and Dave for their time and effort during the past three seasons," Francis said in a statement. "Kirk and his staff worked very hard, but we feel that the team is in need of a fresh start at this time."
The 48-year-old Muller went 80-80-27 in his first NHL head-coaching job after taking over in November 2011.