I used a very similar technique referred to as phytoremediation. This technology was used by the team to cleanup up a site impacted by metals contamination. The primary plant was mustard plant (and there were several other plant species used as well) to uptake contamination consisting of heavy metals in the shallow surface soils. The project was either in Utah or Nevada and the plants needed to not only be drought tolerant, but also grow quickly. The vegetation was mowed every so often, the clippings collected and disposed of. It was a long term project and I recall it worked fairly decent. However, it only addressed the shallow surface soils, how deep, seem to remember not anything deeper that three feet. On another project, I seem to remember using creosote bush to cleanup polyaromatic hydrocarbons. These were both a while back, so the other details seem to obscure themselves, or maybe I just forget more now.
From the mining aspect, I am very sure that some species concentrate various metals better than others. However, the right species in the right place with the right soil chemistry, water chemistry, etc. is what would be required. I would also think that the less reactive the metal, the less opportunity or chance it could get taken up by the vegetation.
The volume of material requiring processing would probably be similar to the undertaking of extracting gold from seawater and probably wouldn't be very profitable at this present time.