In addition to the Hadd punishment, is a person who slanders someone and publishes their slander in newspapers to be punished by Ta'zir?

The specified punishments (hudud) cannot be exceeded or waived once they reach the ruler. For instance, whoever accuses a person other than his wife of adultery is to be punished with eighty lashes, unless he produces four witnesses. Allah Almighty says: "And those who accuse chaste women and then do not produce four witnesses - lash them with eighty lashes and never accept their testimony thereafter. And those are the defiantly disobedient." As for accusations other than adultery or defamation, their punishment is discretionary (ta'zir), determined by the ruler's judgment. If the accused woman is the accuser's wife, the prescribed action is mutual imprecation (li'an).