Hiney and Partridge, whose roles have been made redundant, are in talks about taking other positions within WPP.
As part of the changes, Butler has created three business groups, which will be structured around the agency's clients. Each divisions will be headed by a group head. These are currently being recruited, and will report to Butler.
Partridge and Hiney were promoted to be joint managing directors in April last year.
The roles were created to strengthen the management team as the company sought a replacement for its co-founder and former managing partner Martin Troughton, who left in 2004.
Hiney joined in the same year from Rapier, where he was a business director for three years. His career also includes spells at Modem Media and Tequila Payne Stracey.
Partridge started her career at Ogilvy in the 80s and is a former client services director at WWAV Rapp Collins.
Butler joined the agency in July, just as two of the agency's major clients, Star Alliance and M&G Investments, had left. The agency had already begun to merge with fellow WPP subsidiary Wunderman Interactive.