The former Grant Thornton accountant reportedly resigned from his £124,000 a year post at a board meeting last Friday, leaving immediately without compensation.
The ship builder ran aground after its contract to rebuild the Costa Classica luxury liner was cancelled last autumn.
It sent the company into the red in the first half of its financial year, with warnings issued for its full-year results.
Stafford resurrected the Cammell Laird name when he bought it from VSEL in 1995, two years after the shipyard had been closed down, floating the company in 1997.
Stafford had seen his 25% stake in the company fall from almost £100m to just £8m in the space of 12 months.
Finance director Jon Schofield has temporarily taken on the role chief executive role.
Costa Classica?s owner cancelled the 16-month contract to build the middle section after 12 months when the work had been largely completed.
Cammell Laird said: ‘We have a very strong case and if necessary we will be seeking to recover costs and damages.’
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