The ignore button should be, as it does now already, block out the private messages by specific persons for every player himself and report the person awareness that his messages are not welcome. That already shortens the untoward jabbering a bit.
But the mute button, should definetly cut out anything of the person listed in there, be it the onscreen chat, guild chat or any other messenger possibility.
This is necessary, and should have been added to this game long ago. That would make the game so mutch more enjoyable, its everyone himself, who he wants to read and talk to, and who definitively not.