Mr Bercow said: "In light of the persistent and repeated refusal of the right honourable gentleman to resume his seat when so instructed I order the right honourable gentleman to withdraw immediately from the house for the remainder of this day's sitting".
MPs applauded the infant after Mr Bercow's comments.
Conservatives accused Mr Blackford of orchestrating a publicity stunt because Mr Bercow had agreed to hear his motion for the House to sit in private - which would have required a vote and disrupted PMQs - at the end of the session instead.
Mr Blackford added: "I met with a representative of the United Kingdom government this morning, and I have told them that things have changed".
As Mr Blackford rose again to applause from some of his SNP colleagues, the Speaker shouted: "Order".
At first, the Highland MP did not go.
Every SNP MP followed Ian Blackford out of the chamber as they boycotted the Commons after he was told to leave. Ms Cherry as she left waved to the Speaker, saying: "Goodbye".
And at the end of the questions, speaker John Bercow praised the baby girl who he said had been "a model of impeccable behaviour" despite the "turbulence" of the proceedings.
Tyson Fury beat Sefer Seferi in heavyweight boxing return
Fury played to the crowd in the first round and looked a bit embarrassed when Seferi tried to rough up the former champion. Seferi did a good job of surviving, and Fury struggled to lay a glove on him in the second round.
He called on her to bring forward emergency legislation so that the "will of the Scottish Parliament can be heard and, more importantly be respected".
Speaking later outside Parliament, he said: "The power grab has now in effect happened".
Scottish Secretary David Mundell said the SNP was about to be granted a debate on the devolution aspects of the EU Withdrawal Bill, something which did not take place as a result of the walkout.
He will address MPs on the workings of the Sewel Convention, which recognises that Westminster will not normally legislate on devolved matters in Scotland, Wales and Northern Ireland without the consent of the Scottish Parliament, the Welsh Assembly or the Northern Ireland Assembly.
"We will use parliamentary devices to hold this government to account".
"I have a duty on behalf of my colleagues, on behalf of the First Minister and the government of Scotland and of the Parliament of Scotland, to stand up against the betrayal that has taken place of the Scottish people with the unprecedented power grab which is taking place".
"They are now acting outwith the support of the Scottish people". The Scottish government claims this could prevent it from passing its own laws in these areas for seven years.
But Scottish Conservative MP Kirstene Hair decried the SNP's actions.