Can Earth"s water ever be clean and pure again?

Yes it can, though it may take a very long time but there are filtration processes that can clean the water, however pure is a relative term and cannot be applied broadly. Despite that it can made pure of man made pollution.

Clean and pure water is when there are 2 hydrogen atoms, one oxygen atom and absolutely nothing else. I dont believe it will ever be possible to completely purify earth's water ever again because as humans, we add chemicals like chlorine, and try to distill/evaporate impurities out. This does not result in Clean/Pure water.