Tropes and recurring themes exist for a reason. People are more familiar with the myths being used, so it's easier to communicate the story. Like the OP said, you never write a new story, so the trick is in creating a unique story-telling style instead, like using different gameplay mechanics for the same game. I won't be the same game because it's played differently, but it has the same base storyline, and that's the point.
Now, according to Richard Rorty, you can create new stories (but mainly new ways to conceive the "real" world) by creating new metaphors (giving existing words another meaning), and therefore changing the very language being used to tell the story, and with it the world in wich the story is being told (if you really want to understand it you'd have to read him).
And it's interesting to note that, as seen in his other works, Tolkien made up entire languages, and yet told the same old myths. However, I'd say "The Silmarillion" is very closed to achieving what Rorty talks about, as it tried to describe a world that couldn't be grasped with the language at hand, and just out of need created the metaphors to do it. I'd say this is why that book is pretty dense and hard to understand.
Another close example would've been if Mel Gibson had gotten away with a no-subtitles "The Passion of the Christ", by using a dead language (new meaning to old words) to tell a known story.