Mueller had signed a two-year contract extension last summer. Parcells has a meeting scheduled for Tuesday with first-year Coach Cam Cameron.
The Dolphins completed a 1-15 season Sunday with a 38-25 loss to Cincinnati.
College scouting coordinator Rick Thompson and Assistant Director of Player Personnel Mike Baugh were also let go Monday, the Dolphins said in a release.
"We appreciate the contributions that Randy, Mike and Rick made to the organization and want to wish them well, both personally and professionally, in the future," said Dolphins President Bryan Wiedmeier.
Parcells was hired the week before Christmas to, in the words of Dolphins owner Wayne Huizenga, "help put the Miami Dolphins franchise back among the elite of the NFL."
The Dolphins had a record of 16-32 since Mueller joined the team before the 2005 season. He had been the general manager of the New Orleans Saints for two seasons before joining the Miami team.
This year, the Dolphins lost their first 13 games before beating the Baltimore Ravens and then closing the schedule with losses to New England and Cincinnati.