The Prime Minister said the SNP was guilty of "tunnel vision" in trying to push a vote that would be "bad for Scotland, bad for the United Kingdom, and bad for us all".
It came after Downing Street made clear that the Scottish Government cannot hold a legal independence referendum without the UK Government's approval.
Mrs May said she would trigger Article 50 to begin Brexit "during the next two weeks" and insisted it would be a "great national moment" that will "define the character" of the nation.
But, addressing the Conservative Spring Forum in Cardiff, she accused the SNP of exploiting the vote to leave the European Union.
"The fact that more Scottish voters backed Scotland staying in the UK in 2014, than supported the UK staying in the EU in 2016, and that almost half a million independence supporters actually backed Brexit last year, seems to count for nothing.
"It is now clear that using Brexit as the pretext to engineer a second independence referendum has been the SNP's sole objective ever since last June.
"But it would be bad for Scotland, bad for the United Kingdom, and bad for us all.
"The coming negotiations with the EU will be vital for everyone in the United Kingdom.
"Every person, every family, every business, every community the length and breadth of the United Kingdom - England, Scotland, Wales and Northern Ireland.
"It is essential that we get the right deal, and that all of our efforts and energies as a country are focused on that outcome.
"We can only get that deal if we are united, as one United Kingdom, all pulling together to get the best outcome."
It comes after SNP deputy leader Angus Robertson claimed there was "no doubt" that a second referendum on Scottish independence would take place, despite Mrs May insisting "now is not the time".
Mrs May's official spokesman dismissed the suggestion that the SNP could hold a legal referendum without the PM's approval between autumn 2018 and spring 2019, as set out by Scottish First Minister Nicola Sturgeon.
The spokesman told a regular Westminster briefing: "A legal referendum is a reserved matter."