The 44-year-old Scot, who had only been in the job 10 months, decided to quit after making complaints his efforts to overhaul the business had been made "impossible" by the mutual's failure to reform its governance.
The Edinburgh-born executive, who trained at Coca-Cola, called the organisation "ungovernable" in his resignation letter. He will be replaced by chief financial officer Richard Pennycook who has been appointed as interim chief executive.
Mr Sutherland, who at 6ft 6in is one of the tallest executives in retail, was not feeling quite so elevated after details of the Co-op's proposal to award him a £3.6 million pay deal were leaked.
In a Facebook rant on Sunday, he expressed frustration that the story appeared to have come "from our group boardroom".
He added: "We appear to have disaffected people who are determined to make life difficult and embarrassing for the Co-operative at a time when what we need most are professionalism and loyalty to the business."
The Co-op confirmed Mr Sutherland will forgo a £1.5m bonus and long-term incentive payments due to him for securing the future of the Co-op Bank, which came close to collapse after a £1.5 billion hole in its finances was discovered.
But he still picked up more than £2m in 2013 after earning more than £1m in pay and benefits between May and December, as well as a further £1m in compensation for shares he was due in his previous role as chief operating officer of B&Q owner Kingfisher.
Co-op chairwoman Ursula Lidbetter said she accepted Mr Sutherland's resignation with "deep regret".
She added: "Euan's resignation must now act as a catalyst for the real and necessary change which the group must go through."
In his resignation letter Mr Sutherland said the governance structure of Co-op limited the reforms he wanted to implement.
Mr Sutherland, who has been fronting a campaign to persuade the public to have a say in the future of the 170-year-old mutual, took the helm on May 1, last year, as the scale of issues inside the bank were surfacing.
The Co-op Group had pulled out of a bid to buy 632 branches from Lloyds Banking Group the previous month, two weeks after credit rating agency Moody's downgraded Co-op Bank's debt to junk.
The bank needed to raise up to £1bn to meet regulators' calls for higher capital reserves. Some observers suggested the bank could need a state bailout, a possibility dismissed by the Co-op.
In November the company hit the headlines again after Co-op Bank chairman Paul Flowers was filmed allegedly buying illegal drugs. He remains on police bail.
Mr Sutherland said: "I have given my all to the business and had hoped to be able to lead its revival. However, I now feel that, until the group adopts professional and commercial governance, it will be impossible to implement what my team and I believe are the necessary changes and reforms to renew the group and give it a relevant and sustainable future."
The Co-op last month launched a nationwide poll - open until March 24 - to ask people for their views on its future. The results are expected to be published at the group's annual meeting in May.
In an emergency meeting called last night following Mr Sutherland's resignation, the board agreed to be abolished in favour of a new plc-style board including only executive and non-executive directors, responsible for taking commercial decisions.