What would be amazing would be if clearing an email (or at least marking it as read) on my tablet would get rid of it on my phone as well. Is there anything like this?
If it's Gmail, it should sync and therefore delete the email on your phone automatically, as long as your tablet and your phone are both set to automatically sync with Google. If either is set to manual sync, then you'd have to make sure that you hit the manual sync button on the tablet after you delete, and on your phone to see it delete.