I'm not quite sure what is intended here, but to my mind it doesn't work, not because of the punctuation per se, but that "setting" which is floating unfixed and which no amount of punctuation would ameliorate. I'd suggest as alternatives:
"Behold," said a heavy third voice, setting off a quiet tittering through the group, "each says what they wish to be true."
Though if I were writing it, for this construction I'd probably go with
"Behold!" said a heavy third voice, which set off a quiet tittering through the group. "Each says what they wish to be true."
Otherwise:
"Behold," said a heavy third voice, "each says what they wish to be true." This set off a quiet tittering through the group.
Though again this wouldn't be my take on this construction, as I'd want something more active for the final sentence (though "A quiet tittering ran through the group at this." sounds vaguely Benny-Hill-esque and mildly salacious, so I'd opt for "Subdued laughter" or similar.)