"I say what I mean" implies that you will speak your mind.
"I mean what I say" implies that what you say is what you actually think.
When these two sentences are said together, it means that you speak your mind, no matter what. If, for example, you give someone a compliment, they can believe that what you say is actually true, and you're not saying that out of politeness. I agree that there's some tautology in using these sentences, but trust me, it works when used appropriately. ;-)
John: Mona, you're not only an intelligent lady, but you also look gorgeous.
John: No, I'm not. I only say what I mean, and mean what I say.
PS: I hope Parser will excuse my using "Mona" in the example I came up with. ;-)