Mrs May claimed she "knew from the start" that the SNP leader would exploit EU divisions to revive the case for independence.
But the Prime Minister insisted Scotland's has a "bright future" within the United Kingdom, as she addressed the Scottish Tory conference in Aberdeen today.
The SNP leader last week unveiled plans for a second Scottish independence referendum likely to be held next year in response to the Brexit turmoil. But Westminster has control over the constitution and Mrs May has refused to authorise such a vote. Ms Sturgeon was accused of not respecting the decision of voters.
“Not only does she want to re-run the independence referendum because she did not like the decision of the people of Scotland, she also wants to re-run the EU referendum because she did not like the decision of the people of the UK," Mrs May said "Many Scottish Conservatives campaigned passionately for Remain - but like me, you accepted the decision of the British people and you put your shoulders to the wheel to help get the best possible deal."
The Brexit vote saw a majority of Scots vote to remain in the EU, but the weight of votes south of the border swung the outcome in favour of Leave. The SNP has argued this is a "material change" in circumstances, which justifies a second independence vote.
Mrs May added: "Once again – there’s a big contrast with Nicola Sturgeon and the SNP. On the morning after the vote, before the dust had even begun to settle, before any serious discussions could take place, "The First Minister invited the television cameras into Bute House to put the most divisive issue in Scottish politics, in her words: back ‘on the table.’
"I would have welcomed a First Minister of Scotland who wanted to work with me to deliver a good Brexit deal for the UK.
"But I knew from the start that Nicola Sturgeon was not interested in that outcome.
"She saw Brexit as an opportunity to further her party’s obsession with one thing and one thing only – independence.
"Just imagine if Scotland had a government that put as much energy into improving Scotland’s hospitals as the SNP put into chasing independence.
"A government as focused on boosting Scotland’s economy as the SNP is on internal debates about the hypothetical currency of an independent Scotland."