Phil Dutton, 48, will step down from the board at the annual meeting on 17 December and will leave Britain's largest pubs group at the end of March.
Company sources said his departure was by mutual agreement and that he will receive his contractual entitlement. He was on a one-year rolling contract and his last basic salary was 350,000.
Dyson, who joined the company earlier this summer from Marks & Spencer where he was finance director, said: "I would like to thank Phil for his contribution to Punch over the last three years during which time he played a key role as part of the Board and management team."
Paul Hickman, drinks analyst at broker KBC Peel Hunt, said Dutton's departure was "slightly surprising, but there may have been some overlap with Dyson's former role at M&S."
He added: "Depressed sentiment as a whole on Punch remains on hold ahead of the new chief executive's strategic review findings, which are due in January."
The boardroom change at Punch came as arch rival Enterprise Inns jolted the wider drinks market by saying it would not pay a dividend this year.
That followed a fall in underlying pre-tax profits at Enterprise to 175 million in the year to end-September from 208m the year before amid testing trading conditions.
Enterprise's shares closed off 10.3p at 99.3p, while Punch's shares ended the day down 7p at 61.1p.
Ted Tuppen, chief executive of Enterprise, said: "Given the current degree of market uncertainty, the board does not consider that the resumption of dividends (frozen in May 2009] now would be appropriate." He said he wanted to cut group debt from 3.3bn to 3bn by next September.
Hickman called Enterprise's decision not to restore the dividend disappointing. But he added: "Management comments that we need to see an actual improvement in the trading base, and there are of course many economic headwinds."