laugh away at
1. To laugh heartily and at length (at someone or something). We all sat laughing away at my grandfather's hilarious stories. I love hearing the kids laughing away like that.
2. To pass a certain amount or period of time by laughing. In this usage, a noun or pronoun can be used between "laugh" and "away." Ms. Simpson's comedy routine will have you laughing the night away. Janet and I laughed away the hour trading stories from our childhood.
3. To try to dismiss, neutralize, or ignore something negative by laughing at or over it. In this usage, a noun or pronoun can be used between "laugh" and "away." He tried to laugh away the rude remarks from the audience during his interview. I know you like to laugh issues like these away, but you need to confront them sooner or later.
laugh away at someone or something
to continue to laugh at someone or something. They laughed away at Sue until she fled the room in embarrassment. All the children at the party laughed away at the magician.