Is it right to say 'We didn't say a word that doesn't matter'?
I mean that 'every word we said had a meaning'.
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It's grammatically correct to say it, and the meaning is pretty clear.
But it is not easy to understand what you mean, and it would not be a common way to say it.
It would be more common to say, "Every word we said matters."
Often we can emphasize an affirmation like this by rephrasing it in the negative, "We did not say one word that didn't ...." But in this case, so many typical readers will need to stop and think that you will often completely lose that effect and the opposite will happen: Your point will lose impact because readers will need to struggle to understand it.
In addition, readers very often are not motivated to struggle to understand something, and so may be inclined to just disregard it!
There might be a way to get the best of both worlds. Something like:
Every word we said matters. There is not one that doesn't.
Perhaps something like that is both reader-friendly, and emphatic.
If you want to stick close to this phrasing, two things would help people to understand it better:
We didn't say a word that didn't matter.
By shifting from "doesn't" to "didn't", you keep the tense consistent. I get where you're coming from on "doesn't matter" in that the words still do matter, even though you already said them, but I think that's implied anyway and there's less initial confusion if you just match tenses.
We didn't say a single word that doesn't matter.
This emphasizes that you are pointing out that every single word matters. Without this emphasis there's a possible (less likely, but to some people more immediately accessible) interpretation that you are talking about some specific word. Intonation would help if you were speaking ("we didn't say a WORD that didn't matter" does about the same thing) but in writing you might want that "single."
It depends! If what you're saying is that the words you said continue to matter your form is perfectly correct, though the double negative might be debated. If you are saying that the words mattered at the time and not any more then "We didn't say a word that didn't matter", as suggested by kimberscott, would be more precise.
On the double negative, litotes is used sometimes for emphasis: http://en.wikipedia.org/wiki/Litotes, though Orwell complained about its overuse.