The mistrial request came after it was disclosed at trial that Jones's lawyer accidentally sent two years of the US conspiracy theorist's text messages to the plaintiffs.
His lawyers had sought to explain his absence by claiming that "Jones was remaining at home under his doctor's supervision when, in fact, he was working at his studios and broadcasting his show."
Alex Jones and Infowars media spread claims that the shooting that killed 20 first-graders and six adults at Sandy Hook Elementary School was a hoax, leading to the lawsuit being filed.
A jury in Wisconsin determined the amount to be paid to Leonard Pozner, whose 6-year-old son Noah was the youngest of the 26 people killed at the Connecticut school.
A Wisconsin judge ruled Monday that Pozner had been defamed by authors James Fetzer and Mike Palacek. A trial to decide damages has been set for October.