The SNP Westminster leader questioned the Electoral Integrity Bill, which the UK Government say will protect elections.
Speaking during PMQs, Mr Blackford claimed it was trying to fix “a problem that does not exist”.
He said: "What this bill will do is impose – for the first time – Trumpian Voter ID laws on the UK. The Electoral Reform Society says it could lead to voter “disenfranchisement on an industrial scale”.
“Disenfranchising people from working class communities, BAME communities and other already marginalised groups in society – creating barriers to vote.“Prime Minister – why is this Tory government trying to rob people of their democratic right to vote?”
Mr Johnson insisted it was about protecting democracy, and cited his own personal experience with voter fraud in Tower Hamlets.
He said: “What we are trying to protect is the democratic right of people to have a one person one vote system.
“I think it is important that we move to some sort of voter ID, plenty of other countries have it, I think it eminently sensible and people will be reassured that their votes matter and that's what this bill is about.”
Mr Blackford pointed out there was just 34 allegations of voter impersonation at the last election, and warned millions of people would have their right to vote curtailed under the proposals.
He said: “What this is, is a British Prime Minister seeking to import Trumpian voter suppression to disenfranchise communities that traditionally don’t vote Tory.
“It is a British Prime Minister seeking to make it harder to vote, because it’s easier to get re-elected if the Government can choose their voters, rather than letting the voters choose their government.
“Mr Speaker, 3.5 million people in the UK do not have a form of photo ID, 11 million people do not have a passport or driver’s licence.
“And it’s not just the opposition saying this, members of the Prime Minister’s own party have called his plans “an illogical and illiberal solution to a non-existent problem”.
“Mr Speaker, will the Prime Minister withdraw these vote-rigging proposals immediately or will he continue down the path of a Tin-Pot dictator?”
The Prime Minister accused the Ross, Skye and Lochaber of “making a mountain out of a molehill.”
He added: “Councils will be under obligation to provide free photo ID to anybody who wants it.
“And I do think it reasonable to protect the public in our elections from the idea of voter fraud, nobody wants to see it.
“I don't think that elections in this country should be in any way clouded or contaminated by the suspicion of voter fraud.”
Ministers have insisted the Elections Bill will strengthen the integrity of the process and make it “more inclusive”.
The provisions will apply across the UK in general elections – although similar measures have been in place in Northern Ireland since 2003.