As far as I understand
you should have a button "Dismiss all" in the lower right corner on the "New" tab. Apparently that also untracks the topics though so it might not always be what you want.
In general discourse only marks posts as "new" for 48h (and you can configure this individually in your user preferences which are btw in general fairly interesting as I discovered). And you also have fairly fine control over what categories and threads you are tracking in what way, allowing you to completely mute stuff too. So maybe that is the missing piece of the puzzle here.
I'm still coming to grips with how this forum works compared to what I'm used to, but so far I feel like I just have to learn how this thing "ticks".