清潔（せいけつ） basically only refers to physical cleanliness. Being 清潔 is being free from dirt, dust, blot, bacteria, etc. It's antonym is 不潔（ふけつ）, which refers to something physically dirty.
清浄（せいじょう） is a relatively uncommon word. It can refer to physical cleanliness of water and air in technical contexts (e.g. 空気清浄器), but in non-technical contxts, it tends to refer to more abstract or "spiritual" cleanliness/pureness. The antonym of 清浄 in the spiritual sense is 不浄（ふじょう）, which describes something morally dirty, inpure, corrupted, etc.
Therefore, if you're thinking of the tranquility, sacredness, or any other mental effect of mountain air, 清浄な山の空気 would be the natural choice. If you're only concerned about air pollution or infectious disease, 清潔な山の空気 is also fine.
洗浄（せんじょう） is a suru-verb meaning "to wash", "to clean", "to cleanse", etc. It is basically a kango version of 洗う, and mainly used in technical contexts.