Currently, this setting is only available via desktop, not mobile, so log into your Pinterest account using a desktop browser and go to your Settings.
Scroll Down about halfway through the page or click on Notifications in the left side.
Click on the Pick which group boards you hear about button.
Toggle off individual boards, or toggle Any group board to turn off all notifications.
Click on Save Settings within the board list.
And that's it! Turn that off and you'll stop seeing all of those notifications.