We are not going to make a status of 'a little bit member' or 'not completely', 'pending divorced', 'nearly divorced'.
As the British government distanced itself from a memo including the aim to have the best of both worlds, Bettel told AFP in an interview that Britain could not pick and choose what it wanted.
"They want to have their cake, eat it, and get a smile from the baker, but not the other things," Bettel said on Monday evening in his office in Luxembourg.
"There are European values which cannot be separated. No cherry-picking."
The comments from the centre-right Bettel come as EU leaders step up warnings that Britain cannot expect to keep access to the single market while limiting immigration by European citizens.
British Prime Minister Theresa May has promised to start the two-year divorce process in March 2017 but has not set out her goals, while EU leaders have refused to negotiate until she triggers Brexit.
However in a glimpse of what the British strategy could be, a photographer spotted a memo in the hands of a lawmaker's aide leaving the Department for Exiting the European Union on Monday which included the aim to "have cake and eat it".
It is the latest in a series of culinary Brexit metaphors with British Foreign Secretary Boris Johnson having said "my policy on cake is pro-having it and pro-eating it" and EU President Donald Tusk saying last month: "There will be no cakes on the table for anyone, there will be only salt and vinegar."
But the British memo also suggested Britain will fail to keep access to the European single market and will seek to keep the negotiations to two years, instead of a lengthier interim deal aimed at reducing the sudden impact of leaving.
Last week, Irish Prime Minister Enda Kenny raised the prospect of a transitional deal as it would be "impossible" to finish talks within the two years.
But Bettel ruled out any "hybrid" arrangement.
"What would interim mean? That we are going make a hybrid status now? Either you're a member or you're not a member of the European Union," the Luxembourg prime minister said.
"We are not going to make a status of 'a little bit member' or 'not completely', 'pending divorced', 'nearly divorced'."
"There is no in-between status, there is no hybrid status between the two."
Bettel echoed European Parliament Brexit negotiator Guy Verhofstadt in saying that the divorce should happen before the assembly's next election in May 2019.
"It would be odd to have British candidates at the European elections who will serve for only six months," he said.
The wealthy duchy of Luxembourg, squeezed between France, Germany and Belgium, remains influential as one of the union's six founding member states despite having the second smallest population of any EU state.
While Luxembourg has rolled out the red carpet for businesses that might want to relocate from Britain, Bettel insisted neither his country nor the EU would benefit in the long-term.
"Those are grocer's calculations -- it is not good for Europe, it is a loss when you see the latest figures for Britain, and it's a loss for the European Union," he said.
The rising tide of populism reflected by Brexit, Donald Trump's US election victory and French far-right leader Marine Le Pen's riding high in opinion polls are all warning shots for Europe, Bettel said.
Brexit "is the first step in disunity", said Bettel, 43, who last year became the first EU leader and second in the world to enter into a gay marriage, adding that it "must be a sign for us all".
On the possibility of a Le Pen victory, he said French voters "must make their choice with their soul and their conscience, but they should think carefully to make sure they don't fall into a trap".
As for Trump, who has alarmed Europe with threats to scale back the US commitment to NATO, Bettel added: "I hope and I think that president Trump will be less bad than candidate Trump."