Mr Bercow said he was suspending the party leader for the rest of the day following his "repeated refusal" to take his seat when told to do so.
He stated: "I really do hope that the people of Scotland listened very carefully to what the prime minister said, because the reality of the situation is that powers enshrined under the Scotland Act 1998 are being grabbed back by this parliament today".
He said: "Due to the legislation we passed this week 120 extra powers will be going to Holyrood - this is going to enhance the devolution settlement, not in any way restrict it".
"Yet, last night, she pressed ahead with a power grab in direct opposition to Scotland's elected parliament".
"It is a democratic outrage".
"I asked the Prime Minister to bring in emergency legislation so we can conduct a proper debate, with respect, on the powers of the Scottish Parliament". But the Scottish parliament says Westminster is reclaiming power over policy in devolved regions that the European Union now decides.
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.
What an absolute disgrace. But Scotland's devolved parliament, Holyrood, had rejected those measures last month with the backing of all parties save the Scottish Conservatives. "I will do that".
Blackford concluded: "I have no options but to ask that this house now sits in private". It is not acceptable.
"We need to, we will and we must stand up and defend Scotland's interests".
Just 19 minutes were allocated for debate at Westminster on issues related to devolution during the EU Withdrawal Bill debate last night - 19 minutes during which not one Scottish MP was given the opportunity to speak, the entire time was hogged by cabinet office minister David Lidington.
He used the parliamentary procedure to ensure the will of the Scottish Parliament is respected and that Brexit legislation pauses until the Scottish Parliament's motion is considered as the United Kingdom leaves the European Union.
"We will use parliamentary devices to hold this government to account".
At the end of the stormy hour-long session, Mr Bercow pointed out that Labour MP Clive Lewis's baby, who was in the chamber throughout, had been better behaved.
Looking up at the public gallery with a wry smile, Bercow told MPs in the House of Commons: "For all of the turbulence and discord of today's proceedings, the little baby who has been observing them has been a model of impeccable behavior from start to finish".
The comments were met by cheers and claps from across the chamber.