The 43-year-old leaves his role following Sunday's 3-2 home defeat at the hands of Alfreton Town.
The former Shaw Lane boss, who took over the United reins in November 2017, memorably guided the Pilgrims to the second round of the FA Cup in 2019 and the National League North promotion final in 2020.
Elliott departs the Jakemans Community Stadium with the club's sincere thanks and best wishes for the future.
A further statement will be made in due course.