Mr Bercow said he would be happy to take a vote on the issue after PMQs, but after Mr Blackford repeatedly refused to sit down, he ordered him to leave.
SNP leader Nicola Sturgeon said she was "right behind" Mr Blackford and accused Westminster of treating Scotland with "contempt".
The speaker of the house John Bercow MP appeared flustered and unprepared for the request, at first responding that it couldn't be heard, then stating that it could be, and finally deciding that it would only be heard at the end of Prime Minister's Questions.
She blasted the "farcical" Parliament stating: "The people of Scotland were not able to have their voice heard last night in the European Union withdrawal debate".
That was the cue for Blackford to call for a vote in the House of Commons.
The prime minister's spokesman said: "That sort of stunt effectively means that the SNP members who were down on the order paper to ask the PM questions can't represent their constituents".
'Proceedings on the EU Withdrawal Bill last night were a democratic outrage and the Scottish Parliament must be respected. Again the Prime Minister failed to show respect and denied my request. But the Prime Minister has ignored Scotland.
This is a defining moment for all of us - if the United Kingdom government wants to change course, it must do so immediately by recognising and respecting the will of the Scottish Parliament, the Scottish Government and the Scottish people.
Not only did the anti-Scottish Tories defy the will of the Scottish people - they downgraded devolution, allowing a measly 15 minutes of debate on devolved matters.
Scottish Conservative MP Kirstene Hair said: "This rehearsed move just demonstrated that the SNP care more about headlines than actually achieving anything for Scotland".
They told Sky News: "Scotland will not be silenced and voters are uniting against the brazen Tory power grab".
'The SNP have played games with the constitution, played games with Brexit and now are playing games with Parliament.
Theresa May and her dysfunctional, weak government should be in no doubt - SNP MPs will abide by our duty and stand up for all our constituents and we will do it for a very simple reason.
"Not one single Scottish MP was able to speak in a debate that lasted less than 20 minutes", he said.