I'm curious about whether they will actually bring materials back to Earth. It seems like it would be prohibitively expensive, though perhaps you could construct gliders out of large chunks of titanium and fly them down from orbit cost-effectively, or float small chunks down with balloons.

To me the space-mining industry has always seemed better suited to constructing habitats and vehicles outside of gravity wells like Earth and Mars; part of why it's so expensive to have the ISS is that everything needs to be lifted up from Earth, but if the raw building materials and water (for producing oxygen and hydrogen fuel) were mined from asteroids, then there's less need to go back down to earth for your bulk materials. This would make the second and subsequent generations of mining infrastructure much cheaper to build, and once you've got manufacturing going in space, suddenly the mining becomes a lot easier.

Given a space elevator, there are some neat tricks that help in de-orbiting and orbiting material at the same time. Essentially, you connect two equal masses with a tether, one you want in a higher orbit and the other you want in a lower orbit. With the tether in place, both masses rotate around their common center of mass. When the masses have 'switched' places, you untether them.

I don't recall whether the thethers need to be affixed to the space-elevators to keep them in place.

Gravity

Drop it into a net in the ocean?