As I had mentioned in a comment, there really isn't a way to mass remove notifications unfortunately. You can go through and click them one at a time till they are gone, but as an alternative, you can wait until your next turn. On the new turn old notifications (for the most part) will be gone.
I believe certain notifications stay until you remove them, like who built wonders or players being defeated but I can't say which ones for sure.
As was also pointed out, there aren't really mods for the game that help you clear them faster either.