She warned of "zero credible evidence" to confirm that Scotland will economically benefit from its leaving the single market.
Her remarks came ahead of the publication of the Scottish government's study about Brexit's impact on Scotland's economy.
"Time is running out to prevent the economic disaster of a hard Brexit".
Scottish Government analysis, to be published this week, will set out the impact on Scotland's future economic growth of three options for the future United Kingdom relationship with Europe - if the country can not remain members of the EU.
"Bluntly, the hard Brexiteers have had their chance and failed".
The Scottish government's paper, titled Scotland's Place in Europe: People, Jobs and Investment, also details what it believes to be the benefits of the continued freedom of movement for workers from the European Union.
She said: "It's time for her to stop listening to the discredited voices around her Cabinet table and start listening to the overwhelming case for Single Market membership".
Theresa May has said Britain must leave the single market and customs union to deliver on Brexit
"It will be a fundamental dereliction of duty as Prime Minister if Theresa May continues to pursue her red lines without providing information on their impact and publicly discussing the options available".
"Of course, there is no alternative arrangement that can deliver the jobs, people and economic benefit that come from remaining members of the European Union - but if the United Kingdom continues down the path of leaving the EU, it is the Prime Minister's duty to do as little harm as possible to the economy".
A No10 spokesman said: "We are seeking a deal that works for the whole United Kingdom".
The UK government accused the SNP of "trying to undermine the result of a democratic referendum".
"The Scottish Government is absolutely clear that, if the United Kingdom is indeed leaving the EU, then it must stay within the single market and customs union to prevent needless job losses and cuts in living standards".
"Indeed, as our analysis will show - the harder the Brexit the worse will be the outcome", Sturgeon pointed out.
The Nats' research studies the impact of three different scenarios after we leave the European Union - ranging from staying in the Single Market to a "non-preferential" trade deal with Europe.