The Scottish Secretary insisted the deal agreed by Theresa May on the UK's future relationship with the EU would give Britain full control of its waters after Brexit.
Every Scottish Tory MP, including Mr Mundell, signed a letter to the Prime Minister demanding that access to fishing waters should not be linked to any future EU trade deals.
But the 26-page document published this morning pledges Brussels and Westminster to "establish a new fisheries agreement on ... access to waters and quota shares".
SNP leader Ms Sturgeon said it was a “Tory sell-out of Scottish fisherman” as she urged Mr Mundell to quit the Cabinet.
“What we see is that the Scottish fishing industry will be used as a bargaining chip in wider trade talks," she said. "His position is a matter for him, but if David Mundell is still in office by the end of today, in light of his political declaration, he will have forfeited forever any last remaining scrap of principle or credibility that he had."
Scottish Tory MP Ross Thompson also savaged the deal, which he said "means sovereignty over our waters sacrificed for a trade deal. That is unacceptable. We must be a normal Independent coastal state like Norway".
But Mr Mundell hit back on Twitter, insisting he was "not taking lessons on standing up for fisherman from Nicola Sturgeon who is committed to trapping them in hated (Common Fisheries Policy).
“The PM has fiercely resisted the efforts of EU States to make an explicit link between access to our waters and access to markets. We will negotiate and decide, as an independent coastal state, on access and quota on an annual basis just like Norman and Iceland do now.
“The surest way to guarantee the EU access to Scottish waters would be to rejoin the CFP – exactly what Nicola Sturgeon is demanding."
In a boost for the Government, Bertie Armstrong, chief executive of the Scottish Fishermen’s Federation, welcomed the latest Brexit deal.
He said: “The declaration gives the UK the power to assert its position as an independent coastal state with full, unfettered sovereignty over our waters and natural resources.
“However we know that several EU nations will not give up their attempts to link access with trade in order to retain absolute rights to fish around our coastline.
“So we will continue to seek assurances from the UK Government that it will remain steadfast and will not rest until the future arrangements are signed, sealed and delivered and we secure that critical control over access to our waters and who catches what stocks, where and when."