Griffiths, who joined Royal Mail Letters as managing director in February 2006, is understood to have quit after the board rejected his business proposals.
According to sources, Griffiths objected to the government's plans to enforce around £300m worth of cuts across operations. The cuts come ahead of the rising automation of the Royal Mail's business.
In the meantime, Adam Crozier, chief executive, will take on the handling of Royal Mail Letters, which tops 20bn items annually, until a permanent replacement is found.
Griffiths' departure follows a spate of recent senior management exits from Royal Mail, including David Flowers, head of property, who left in January this year, Marisa Cassoni, finance director, and David Mills, head of the Post Office division, who both left last year.
Prior to joining Royal Mail, Griffiths was group managing director at GKN Automotive.
Earlier this month, Royal Mail lost a High Court appeal to reduce the size of a £9.62m fine imposed by Postcomm for failing to adequately protect mail in its care and having ineffective systems for preventing lost mail.
Earlier this week, Royal Mail handed its £18m media account to OMD, following a pitch against incumbents Carat, which have held the account for the last 10 years.
A Royal Mail spokesman said: "We will be looking for a new person for the role going forward."