John Bercow ordered Mr Blackford to leave for standing and repeatedly calling for parliament to sit in private.
The speaker told him a vote would be called on it but only after Prime Minister’s Questions had finished.
Mr Blackford refused to let the matter rest, saying multiple times: “Scotland will not be disrespected by this parliament.”
The speaker shouted “very well” and waved his hand as three benches of SNP MPs rose in protest, with choruses of “bye” – although it was unclear from whom.
“What a pity, because there are SNP MPs who had questions on the order paper,” Mr Bercow said afterwards.
SNP leader and Scottish first minister Nicola Sturgeon tweeted minutes later that she was “right behind” her party’s MPs.
She claimed Scotland and Holyrood were “being treated with contempt by Westminster – and it needs to be highlighted”.
Mr Blackford spoke to the media from outside parliament afterwards, claiming it was “no stunt”. An SNP source also told Sky News the protest was “spontaneous” and not pre-planned.
The Ross, Skye and Lochaber MP called votes on devolution amendments to the Brexit bill last night a “power grab”.
He attacked the UK government for giving around an hour to discuss one amendment on Northern Ireland, followed by votes on more than 50 devolution issues, which the government won,
“Where is the respect from Westminster towards Scotland?” he asked.
But Alberto Costa, a Tory MP and adviser to the Scotland secretary, called the move “an embarrassment for Scotland”.
“They abused the proceedings of the House of Commons with this ridiculous stunt,” he told Sky News.
A Number 10 spokesperson also 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.”
It came after a heated clash between Prime Minister Theresa May and Labour leader Jeremy Corbyn, ahead of more votes on amendments to the EU Withdrawal Bill imposed by the House of Lords.
Downing Street said immediately after that it would table its own amendment to be debated by peers next week, responding to rebel MPs’ concerns.
But Mrs May’s spokesperson added it was a “fair assessment” that a key clause of backbencher Dominic Grieve’s suggested law change was “not up for discussion” – contrary to the promises allegedly offered in a meeting with the PM on Tuesday.