Assistant Coach Rod Brind'Amour will remain part of the coaching staff.
This is the first major move for General Manager Ron Francis since being appointed to the position last week.
"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."
Muller, 48, compiled a record of 80-80-27 during three seasons with Carolina after being named head coach on Nov. 28, 2011. It was his first head coaching position in the NHL.