This concept (that I would not support, by the way) is called "Freudian slip", applied to speech. I cannot recall any corresponding saying in English. But I think an acceptable translation might be: "Slips of the tongue reveal the truth."
Thanks for this gianis167. I came across it a few months ago in Ελληνικά στα Βαθιά. We don't quite have a saying for this. The nearest I've managed to come up with is "a slip of the tongue gives the game away". This isn't quite a "saying" but almost. We could but probably wouldn't say it as a generalisation, as I think you do in Greek. It is more a response to what we are now learning to call someone "mis-speaking" . We are slightly more likely to use it in the past tense which makes it not a saying at all. You could equally also say "gives/gave him/her/it away". Or even "me/you". How would you say that in Greek? ?Something with προδίδω??
If you wanted to create a genuine sounding English saying you couldn't get better than the διαφορετικός version!