He hit two buttons together. Probably 'play' and 'record.' he didn't erase the tapes, he taped over them with Soundwave's friggin' cylon voice whining about it.
A strong magnetic pulse will erase a tape in an instant, though why Soundwave would keep that on his abdomen is your guess.
He was a Saturday morning villain - they all had some sort of weakness so they could be brought down like that when the episode reached the last five minutes. I mean, in Headmasters, Blaster also had to bring down Soundwave in their third and final duel - he put his fist through his chest. Pretty brutal, that fight. Their first fight, Auto-Bop, was a good one too, and was one of the few times Soundwave laughed. Or am I thinking of Jazz in that scene? Either way, they used sound as a weapon there, but in a much more effective and interesting way. Season 3 Soundwave was very watered down compared to how he had been early on.