When you laugh someone down, you cause someone to quit something he is doing. You force him to give up . You do it by laughing at the individual. In other words, you ridicule the poor guy.
Examples: ”The poor guy was laughed down by everyone in the audience.” * ” Hari gave up the idea of becoming a singer after his audience laughed him down.” * ” The little children laughed down the magician’s act.” * ” Teja gave up the idea of becoming an actor when her performance was laughed down by her own family members.”