The former midfield stalwart returned to the club in 2018 to replace club legend Chris Kinnear.
But it has been a difficult few years and the club have been inconsistent since their return to the National League South.
Their New Year’s day defeat to Dulwich means it is just one win in eight.
Player Mitch Brundle and coach Mike Sandmann will take joint interim charge against Hungerford Town on Saturday.
Chairman Jim Parmenter told the club’s website that he is sad to see him go.
He said: “Andy has given terrific service to the club and assisted me in navigating some very difficult times.
“I wish to place on record our gratitude for his efforts, understanding, and hard work during his time at the Club.
“He is a man of integrity and decency, and I am sure he will be successful in his next role.
“We remain good friends and Hess will be welcome at Crabble at any time.”