Mining is not exactly a natural process. We can't dilute the toxic byproducts and putting them back where we got them, since that would require rebuilding the mountain. In cases of open mines, all that is left is a lake size hole where solid land once where.

What the mining industry do is to fence it up (including pools used for waste), put up a sign to warn people, and then let nature fill it up with water. The best we can hope for is that they did their research properly and made sure that it doesn't leak into the groundwater.

In the past there were people who tried diluting stuff like this by dumping it into the ocean, but that isn't the best idea.

Uranium came out of the ground as well, and there were natural reactors.

Nuclear waste does not consist of Uranium, but of the much more radioactive fission products. The Okla natural reactor went critical for the last time around 2 billion years ago. Indeed, nuclear waste is not a problem if you can wait for 2 billion years.