Speaking in what she dubbed Scotland's other 'yes' city - Dundee - she said most of Scotland was "heartily sick of Brexit and of the chaos we have seen play out at Westminster night after night."
But the First Minster of Scotland said if Brexit goes ahead then the three years after the EU referendum would have "just been the warm up act."
"Trade talks for the future haven't even started yet and given the hard line approach of Boris Johnson, especially now with Nigel Farage pulling his strings, there is every chance that Scotland will be forced out of the EU next year with no trade deal at all," Ms Sturgeon added.
She said the "future of Scotland" was on the line at this election and urged the nation to back the SNP.
"The truth is Westminster is going to be enfulfed by Brexit chaos for years to come, with long term damage to Scotland guaranteed," Ms Sturgeon said.
"That is why my message is clear, a vote for the SNP in this election is a vote to escape the mess of Brexit."
"For Scotland, the question the debate posed is this: why should we be content for either of these men to run our country and shape our future, we can do so much better than that," the First Minster of Scotland said.
She said "incredibly" Jeremy Corbyn has not said whether he want to remain in the EU or leave during the televised debate on Tuesday.
The overall tone of her speech was a vote for the SNP was a vote to escape the control of Westminster.
Ms Sturgeon said Scotland had been subjected to Tory austerity and claimed by the end of the decade Westminster will have cut Scotland's budget by £1.5 billion in real terms.
In contrast, she said Scotland has prioritised NHS investment, and other public services, over tax cuts for the rich.
The SNP has abolished NHS prescription charges and protected free personal care for older people, which she said was a "Scottish model for public services."
And she said free tuition fees for Scottish students was a "reality the SNP will always protect."