Turning to the speaker, he said: "Under the circumstances, given the disrespect shown, I have got no option but to ask that this House sits in private".
Speaking to the BBC immediately after the incident, Mr Blackford said: "Scotland's voice has not been heard, we have had changes to the devolution settlement that were pushed through last night without Scottish MPs voices being heard".
Mr Bercow shouted "not now" and demanded the SNP chief resume his seat - eventually expelling him for the rest of the day when he refused.More news: KKR nears agreement to acquire Envision for about $5.5 billion
The SNP MP told the same programme: "He ought to resign and the fact we have seen powers taken from the Scottish Parliament and our elected representatives have not been able to debate this is an utter, utter disgrace".
"It is a democratic outrage".
The unprecedented event brought PMQs to a temporary halt as Mr Bercow refused his demands.
Opponents said the move was planned well in advance, taking place during prime minister's questions, the highlight of the parliamentary week.More news: Trump Suggests Singapore Summit Ended North Korea Nuclear Threat
The passing of the EU Withdrawal Bill meant powers which were supposed to return to the Scottish Parliament after the United Kingdom leaves the EU would go to Westminster for a period of seven years, a move which SNP MPs broke with the Sewel convention that changes to devolution would not occur without the consent of the Scottish Parliament. My mixed sequence of advice is that is better for the vote to be conducted at the conclusion of questions to the prime minister... It leaves Holyrood exposed to having powers taken without consent in areas including trade deals, environmental standards and food safety, all issues of key concern to the Scottish parliament and all of which impact detrimentally on Scotland's economy - we're talking a loss of up to 80,000 jobs and cuts to wages of £2,000 a year, according to economists.
He added the issue would "haunt the Scottish Tories for a generation". But Scotland's devolved parliament, Holyrood, had rejected those measures last month with the backing of all parties save the Scottish Conservatives.
During today's PMQ's, SNP Westminster leader Blackford said Brexit was being used as a "power grab" from the Scottish Parliament and branded last night's debate a "democratic outrage".
SNP leader Nicola Sturgeon has said she was "right behind" Blackford and accused Westminster of treating Scotland with "contempt".More news: Singer, 13, earns Howie Mandel's golden buzzer on America's Got Talent