Alexandra, I like your questions as they so often challenge a native speaker's way of thinking.

I have never heard of a blunt accent, or a "blunt saying".

The normal meaning of blunt is either the opposite of sharp (as in a knife) or when one speaks bluntly, which means to speak very openly, or not to "beat around the bush" but just to say what you mean.
There is such thing as a polished accent, which an aristocrat might obtain by going to the right schools etc.

The opposite would be an unpolished accent, i.e. a crude or even vulgar accent that reflected little or no education, likely to be found in peasants or people of"low birth".

I guess it might also be said of the accent of a person speaking a foreign language, but that woud depend on how/where/ they had learnt the language.

is another possible interpretation. E.g., many English speakers find a strong German accent to be 'pushy', perhaps mostly due to 6 decades of Hollywood propaganda, from Colonel Klink to the Arnie S.

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Note added at 11 hrs (2011-02-02 09:53:50 GMT)
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But given Alexandra's complete lack of context - who knows??

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Note added at 12 hrs (2011-02-02 10:04:54 GMT)
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perhaps a reference to Emily Blunt's accent, you know, a blunt accent...

Working class, colonial or foreign English. The English might be good, but it may lack that 'sharpness'. I would imagine this question has something to do with England.

This is particularly likely if this is about somebody from the North of England. In fact Northerners are generally quite proud of being or sounding "blunt" and it is often used as a compliment. Northern English accents do have a particular sound that is well described this way and which is often considered attractive and reassuring, which is why call centres are often located in the North of England.

"Gawn Grainger and Richard Johnson turn in a fine pair of performances as the Mann brothers and Lizzie McInerny plays Nelly with a blunt northern accent. ..."
www.compulink.co.uk/~shutters/reviews/01147.htm

"Emperor Kev (With a blunt Northern accent) : New coloured lights, new steps at Oyster Cove, new loos, new bins, extra street cleaning, 'ey by gum! ..."
www.torbay.gov.uk/byethebye-06102008.doc

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Note added at 12 hrs (2011-02-02 10:33:37 GMT)
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'"Shakespeare sounds terrific in authentic northern voices"
Daily Telegraph

"The Northern voice, with its short blunt vowels and tactile concrete consonants, makes a sensual meal of language, quite unlike the icky snacking gone in for by some of the more clipped southern accents."
The Independent'
http://www.northern-broadsides.co.uk/PAGES/ABOUT_US/aboutus_...

See also the obituary of dancer, choreographer and writer Terry Gilbert:
'"He had a forthright manner and a blunt northern accent that in his early days earned him snobbish comments. "Many," he wrote, "noting my thick Derbyshire accent, were convinced that it was a miracle I managed a career at all."'
http://www.independent.co.uk/news/obituaries/terry-gilbert-7...