There are 13 Tory MPs in Scotland, but the YouGov poll for the People's Vote campaign indicates they would all be replaced by the SNP.
The polling, which was conducted exclusively in Conservative-held constituencies across Scotland, points to a 14% drop in the party's vote share in these seats, down from 44% to 30%.
Meanwhile, the vote share for the SNP is predicted to rise from 34% to 42%.
The poll shows a majority of voters in these constituencies would vote to keep the UK in the EU in a new referendum, by 63% to 37%, excluding non-voters and don't knows.
More than half (51%) back a new public vote on Brexit, rising to 58% when don't knows are excluded.
About a third (33%) of those questioned back leaving the EU with no Brexit deal if Parliament continues to vote against a withdrawal agreement.
Pollsters also found more people oppose a general election before October 31 than support the idea of a poll before the Brexit deadline, at 37% to 41%.
Questioned about the impact of Brexit, respondents believed by three to one it would leave the economy weaker (53%) rather than stronger (17%).
By almost seven to one those polled said Brexit would leave their family worse off (48%) rather than better off (7%).
A similar ratio thought the NHS would get worse (48%) rather than better (13%).
By almost 10 to one those polled believe Brexit will lead to higher taxes, at 48% to 5%.
Half of respondents (50%) think the next generation will be left worse off by Brexit, with just 15% believing the opposite.
Lord Cooper, previously pollster to former Scottish Conservative leader Ruth Davidson, said: "This poll sends a very serious warning to the Conservative and Unionist Party in Scotland.
"Boris Johnson's threat to them is not that he will be a bump in the road on a slow but continuing recovery, but that he will effectively eliminate them overnight as a major force in Scottish politics, and so reverse ten years of patient hard work by Ruth Davidson and hundreds of hard-working volunteers, councillors, MPs and MSPs.
He added: "Asking Scottish voters to choose between their British and their European identities, and forcing Scottish voters to back a nationalist agenda that might work in some parts of England, looks as though it will spectacularly backfire."
SNP Westminster group leader Ian Blackford said: "This stunning poll underlines the strength of opposition to Brexit in Scotland.
"Boris Johnson's reckless plans for an extreme Brexit would be devastating - threatening to destroy 100,000 Scottish jobs and inflict lasting harm on living standards, public services and the economy.
"It is shameful that Scottish Tory MPs have completely failed to oppose them."
A total of 887 Scottish adults were questioned between August 28 and September 4.
A Scottish Conservative spokesman said: "The Scottish Conservatives are the only opposition to the SNP.
"Time and again the SNP has used Brexit to push for another divisive independence referendum.
"The Scottish Conservatives are the only party which respects the outcomes of both referendums."