In the official app notifications are visible by clicking the bell 🔔 icon at the bottom of screen. Make sure you've clicked "everything" at the top if you want to see every notification.
Once you view the notifications in "everything" mode, it will mark them as read and the dot will disappear.
You can't clear notifications on the official app, but if you log in via your server's website (https://mastodon.art) there is a "clear notifications" option at the top of notifications.