Is the sentence "I saw him saying..." right?

Both sentences are grammatical but mean different things. One uses one's eyes to see the images and one's ears to hear the sounds involved in this case.

Both could be used, but it largely depends on the context. Let's say you are a in a court of law as a witness. A prosecutor could ask you:

You just stated you heard him saying that. Did you personally see him (pointing at a defendant) saying that to the Chairman?

You could answer:

Yes, I (personally/in person) saw him saying that to the Chairman.

This conversation might not take place very frequently, but is not impossible.