It was rare to see Roxas smile, even rarer to hear him laugh. According to Roxas he had no heart, so that meant that he had no emotions. Laughter was an emotion and thus required a heart.
Axel just figured that Roxas didn't want to laugh. He was certain that Roxas could laugh if he really wanted to.
Roxas never seemed to want to do much of anything around Axel anymore. Not since he found out that Axel knew why he had keyblades but never bothered to share this information with Roxas.
So Roxas stopped showing emotions all together, as punishment.