Click on your username in the blue navigation bar at the top right corner of the screen. From the drop down menu, choose Preferences. You'll see an option for Push Notifications - click on the button to block/allow those notifications. These instructions assume you're using a PC - if you're using your mobile phone, you just need to ensure you're logged in to Mazda247, then click on this link to access your Preferences page.
If you scroll down further on that page, you can also specify what type of notifications you'd like to receive for certain actions (in case you do want to receive notices for things like conversation messages only).