This seems like a relatively simple thing to do for the system yet there are no options?
You can click the X next to a notification to dismiss it but you can't fully turn it off. But, I do know of a feature that might help. If you have multiple sections in a course it's possible to set an enrollment to only be able to interact with people in the same section. For a teacher this would mean you'd only see students in speedgrader and get notifications for students in the same section as you. To set it this way to People in the course, find yourself and click on your name. In the area where it lists your enrollment there should be a link saying something like "limit this user to only see fellow section users". Give that a shot and see if it does what you are wanting. I know I've see the feature used a lot to limit TA access to just students in their sections.
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