Peter Chapman issued the warning as Holyrood’s Rural economy Secretary Fergus Ewing prepared to travel to Brussels for fishing quotas talks - with the discussions to be the last the UK will take part in before leaving the European Union.
Mr Ewing said Brexit had “loomed large” over this year’s quota talks - which could mean permitted catches for mackerel, cod and haddock are cut.
Mackerel quotas could be down by 20%, while the cod catch could be reduced by 33%, with haddock facing a slightly smaller reduction of 31%
While Scottish ministers have raised concerns Theresa May’s draft Withdrawal Agreement could mean the Scottish fleet is “sold out”, Mr Chapman insisted it was “pragmatic and workable”.
The Conservative said: “We are the only party working hard to deliver on the instructions of the people to come out of the EU and to take control of our borders, our money and our waters.
“And that means coming out of the CFP and taking the shackles off our fishermen.”
With Nicola Sturgeon having made clear “that she wants to stop Brexit in its tracks” Mr Chapman said the message to fishermen was that “the SNP will do everything they possible can to keep you in the hated CFP”.
He said: “Our fishermen will never forget and never forgive the SNP if they prevent us from leaving the hated and discredited CFP.”
Mr Ewing said his aim at next week’s talks would be to “resist cuts where there are scientifically justifiable reasons for so doing”.
He told MSPs: “Technically this year’s talks have been business as usual, given we are still a member state, however, as expected the wider scenarios still in play around Brexit are having some upstream influence on what we may expect to achieve at this year’s talks.
“This may make things more difficult but potentially it could give us a lever we haven’t had before.”
He also said he would speak out for Scotland’s fishing sector when the UK is negotiating its future relationship with Europe
“It’s imperative that Scotland’s voice is heard when the UK is establishing a deal on fisheries relations with the EU,” the Rural Economy Secretary said.
“It’s my intention to champion the views and priorities of the Scottish industry in any and all scenarios.”
Labour’s Rhoda Grant stressed the importance of ensuring the “pantomime that is Brexit doesn’t distract us from some of the big issues surrounding the negotiations”.