Ian Blackford said the review, which will be announced by the Prime Minister in a speech in Scotland tomorrow, was an act of “sheer desperation”.
But Mrs May hit back, saying it was the nationalists who wanted to dismantle the devolution settlement by pursuing independence.
The Prime Minister also claimed there was “no review of devolution”, despite one of her ministers going on the radio just hours earlier to talk about it.
Scotland Office minister Lord Duncan said the review, which will be led by his predecessor Lord Dunlop, was a “simple straightforward way of making sure devolution is working as best as it can be”.
Lord Duncan told BBC Radio Scotland’s Good Morning Scotland programme: “What we’re doing right now is examining how devolution works here.
“Time and time again I’ve listened to the First Minister saying that the UK Government isn’t working for Scotland. The UK Government is working for Scotland and it wants to make sure that it is working as best as it can, hence this review - a simple straightforward way of making sure devolution is working as best as it can be.”
He added: “What we’re trying to do now is make sure the governments of Scotland work in Scotland’s best interests.
“The important thing here is the union is at the heart of this government, it believes passionately in that union and it wants to make sure that the governments of Scotland work together.”
At Prime Minister’s Questions, Mr Blackford asked Mrs May whether she thought “the future of Scotland should be decided by the people who live and work there, or by her party”.
“This Prime Minister’s days are numbered,” the SNP leader said. “Her review into devolution is nothing more than an act of sheer desperation.
“This is a Prime Minister running scared of the people of Scotland.”
Mrs May said that the future of Scotland “was decided by the people who live and work there... in 2014, and they decided they wanted to stay as part of the United Kingdom.”
Citing a single poll that showed 53% of Scots would back leaving the UK if Boris Johnson becomes Prime Minister, Mr Blackford claimed that “if the Prime Minister looked at the opinion polls she would see there is a majority for independence”.
He went on: “This review is a farce. The real legacy of this Prime Minister is shutting down Scotland and ignoring the will of the Scottish Parliament. The Tories have never supported devolution and it’s clear they never, never will.”
Mrs May replied: “There is only one party in this house who wants to stop devolution in Scotland, and that’s the Scottish National Party.”