Everton insisted manager Rafael Benitez retains their "full support" amid an ongoing slump, but director of football Marcel Brands has left the Premier League club.
Dutchman Brands joined Everton from Eredivisie outfit PSV in 2018 and signed a new three-year contract as recently as April.
Reports emerged on Sunday he had left his Goodison Park post and that was made official late in the evening, with Brands saying it was his choice to move on.
Brands departed due to differences in opinion over plans for the future of the club, with his views apparently not sufficiently aligned with those of others.
He said, quoted on Everton's website: "This decision has taken some time and some consideration and was one of the most difficult I have faced in my career.
"The board and I agreed that there is a clear difference in the vision and direction for this beautiful club and, with that in mind, the decision was taken."
Everton are mired in a dismal run of form under former Liverpool boss Benitez, taking one point from a possible 21 across their last seven games to slide out of the top half and down to 16th place.
In a statement, the club said: "Everton Football Club can confirm that Marcel Brands has left his post as director of football.
"Brands joined Everton from PSV Eindhoven in June 2018 and was appointed to the club's board in 2019. The owner and directors would like to thank Marcel for the service he has given to the club over the past three and a half years and wish him well for his future.
"A strategic review of the football structure will now take place which will inform the best model for the club to proceed with in the long-term.
"In the meantime, the owner and board of directors will continue to provide our manager, Rafa Benitez, with their full support."
Everton's owner is Farhad Moshiri, who elected to appoint Benitez after Carlo Ancelotti left the club at the end of last season to embark on a second spell as head coach of LaLiga giants Real Madrid.
A 4-1 defeat to Merseyside rivals Liverpool last Wednesday was Everton's last Premier League outing, with Benitez's team next in action on Monday when they face Arsenal at Goodison.
The appointment of Benitez in June was a controversial one given his past as a fans' favorite at Liverpool, and his renowned affection for the Reds. A positive start curried favor with some skeptics, but there has been a cooling in the support from many Everton supporters for the Spaniard and his team in recent weeks, with results in a sharp decline.