When you sign up for the OnSong Beta Team, you're added as a tester into a program called TestFlight operated by Apple and the App Store. That means that you will receive notifications when new versions of the app you are testing are available.
To stop receiving notifications from TestFlight, open the TestFlight app on your device and choose the app from which you are receiving notifications. In the App Information section, you'll find two switches for Push Notifications and Email Notifications. You can choose to turn these off to stop receiving emails and push notifications on the device respectively.
If you no longer want to be a member of the beta team, you can tap on the Stop Testing option in red at the bottom of the page. This will also stop sending notifications. Please note that the app you are testing will stop functioning once you leave beta testing.