Why he stutters is a big question in 1x02 "Compulsion". It's kind of explained at the end when Elle tells Gideon that she's checked and found out no one knows what causes stutter. So she believes he was just buying time with the conversation. Gideon doesn't deny or confirm that but from that what follows one can assume she was right.

thank you for your reply. Is there an episode where you see more of what happened with Gideon and that man?

You're welcome. :) No, it all ends in Compulsion. They never went back to that story again.

That's the ending of Series 1, Episode 1. Only briefly re-visitied in the opening scenes of 'Compulsion' (Episode 2).