The First Minister unveiled the party's manifesto in Glasgow today with a warning that a "hard" no deal Brexit remained a possibility and would be disastrous for Scotland.
The SNP is demanding the right to hold a second referendum on independence next year, but this has been rejected by Boris Johnson, while Jeremy Corbyn has ruled out such a vote in the early years of a Labour Government.
But Ms Sturgeon said: "I think people are becoming increasingly sick of hearing Jeremy Corbyn and Boris Johnson talking about not allowing Scottish people to choose our own future," the SNP leader said at the manifesto launch in the west end of Glasgow.
"Well I've got news for them - it's not up to you. It's a decision for the people of Scotland and for the Scottish Parliament.
"The democratically elected Scottish Parliament has agreed that the people of Scotland should be given a choice over their own future. An unelected Tory Westminster Government has not right to overturn that decision.
"So, an SNP victory at this election would be a clear instruction from the people of Scotland to respect Scottish democracy.
"So in this election, you can vote SNP to the strongest message to Westminster, to Boris Johnson and to every Westminster politician - There must be not Westminster veto over the right of the people of Scotland to decide their own future."
Ms Sturgeon described this as the "most fundamental of democratic principles" and warned that the SNP would not support a Labour-led administration after a hung Parliament without Mr Corbyn granting a section 30 order which would give Holyrood the power to stage a referendum on leaving the UK.
She added that Scotland now stands at a "crossroads" as the the prospects of an "extreme Brexit" looms under Boris Johnson.
"People in Scotland have the right to consider an alternative future, one in which Scotland's future is in Scotland's hands, not in Boris Johnson's hands."
The SNP leader added that the leaders of the pro-union campaign, made up of the Westminster parties, promised that a No vote would lead to stability.
"Since then, the Westminster parties have delivered not stability, but constant chaos and three UK general elections," she added.
The election manifesto states that if the SNP win the most seats in Scotland it would send a "clear" message that an independence referendum must be held next year.
She added that Scotland will pay a price for the Conservatives' "obsession" with Brexit and Labour's "woeful lack of leadership".
She said the SNP backs a new, UK-wide referendum on EU membership.
But she added: "Jeremy Corbyn, incredibly, says that he is neutral on the issue of Leave or Remain.
"That means he is neutral on job losses, cuts to living standards and the erosion of our rights.
"And, of course, he would be happy to sit back and see Scotland taken out of the EU, even if there is a majority for Remain in Scotland but not in the UK."
The First Minister reiterated her assertion that Brexit will "dominate" Westminster in the coming years, adding "Scotland will pay a heavy price for the Tories' Brexit obsession and Labour's neutrality, or to give it its proper description, Labour's woeful lack of leadership."
She said Scotland's future is at stake in the General Election, asking Scottish voters to consider who should decide the future of Scotland - "the people of Scotland, or Boris Johnson?"
She said she is open to forming a "progressive alliance" with other parties following the election.
But she added: "Unlike the Liberal Democrats, the SNP will never, ever help the Tories into government, but we will be prepared to talk to other parties about forming a progressive alliance.
She demanded more UK government investment in the NHS and a "real end to austerity".
She said: "A potential UK government that wants our support must reverse that cut to our budget and ensure real-terms growth thereafter.
"A party seeking our support must be prepared to set out how they will repair the damage of a decade of austerity and put back the money that's been lost."
Ms Sturgeon told the audience her party would "stop the Tories from selling off Scotland's health service".
And she said "policies which are driving people into poverty" must be scrapped.
Attacking the Conservatives for providing extra funding for the DUP following the 2017 general election, she said: "Remember when the Tory government last needed a handful of votes from the DUP, they bypassed the Barnett Formula to find money for Northern Ireland.
"In the process they denied Scotland around £3 billion of investment.
"We say enough. It is time for Scotland to be treated fairly."