If you just mean the "show new replies" link. You'd have to look at the new post in order for the "new" to go away, That or you can read those you want and then click "Mark all messages as read". This will clean up the whole list ofc.
But if you mean as in that email notification I'm not too sure, I know there's submenus inside the profile that lets you set if the forum should notify you of new replies or not, maybe even a list of threads you're watching. Not too certain since I haven't used this function myself.
