The duo has also scrapped the agency's board of 84 - which equates to almost one in three of the 300-strong staff - in favour of a more nimble management team numbering not more than 20.
"We are going through a restructuring of the agency and the way we work. Martin has been here for many years and has decided that, moving forward, he wouldn't be part of the new team," Dundas said.
"A large board was fine in the old days but the numbers involved make for a ludicrous statistic. It is not a cost-saving exercise, all the benefits remain in place, but people have a different value system now and we are looking at more modern ways to recognise value and achievement."
Rory Clayton, Saatchis' head of operations and the former head of recruitment marketing for the Army, has also left the agency. Clayton joined in 1999 to set up a special unit, called Flying With Geese, to help companies inside and outside the Saatchis network to raise morale and manage change.
The appointment of the low-profile Cotter to the group chief executive role in October last year came as a surprise to the industry. He was formerly the managing director of The Facilities Group, Saatchis' production operation.
Cotter is famously publicity shy and when asked for a photograph to accompany an interview once said: "I am not having my photo taken. Why don't you use a picture of that fat bloke from TBWA instead?"
Saatchis' is currently seeking a managing director to complete its senior management line-up.
Dundas was promoted from managing director to the top post last month following the announcement that the chief executive, James Hall, was leaving the agency to return to his native New Zealand.