The only reason that nuclear waste from fission is even an issue here in the United States is that our government refuses to allow the reprocessing of spent fuel, because for one brief step in that process, bomb-grade plutonium is produced before being mixed with uranium-235 and less fissionable isotopes, typically uranium-238, to form mixed-oxide fuel. We are the only nuclear nation in the world to not reprocess our spent fuel. (Former President Jimmy Carter made the executive order on this.)
The remainder of spent fuel is various daughter products of (primarily) U-235 and Pu-239 fission. These isotopes have much shorter half-lives than conventional nuclear fuels, and after ten or so years are pretty much harmless.
Fusion power is not entirely free of waste either. Deuterium-tritium fusion, which is much easier to start and control than deuterium-deuterium fusion (I won't even bring up helium-3-deuterium fusion, as there are no viable He3 sources nearer than Jupiter), produces helium-4 and a neutron as the fusion by-products. These neutrons collide with the steel shielding, specifically designed to trap them. However, over time, enough neutrons collide with the steel that it becomes radioactive, which brings us back to the radioactive waste problem of fission, except this waste can't really be reprocessed into anything useful, until it decays to negligible levels, which, depending on what isotope of iron it reaches before it begins decaying, could be millions of years.
As for obtaining the fuel for fusion, this can be done entirely automatically by extracting heavy water from ocean water, electrolyzing it, and then separating the hydrogen isotopes. Protium would be reacted with the oxygen and released back to the ocean, while deuterium and tritium would be stored for fusion. This process is even safer than mining uranium, because there are almost no workers involved.
I need to go find my bibliography...