Both clean and cleanse can be used to mean to remove dirt or filth from. But clean is more often used literally, and cleanse is more often figurative. So cleansing is often spiritual or psychological, while cleaning is usually sanitary or cosmetic.
Meanwhile, cleanse has two others meanings it does not share with clean: (1) to remove a group of people from an area, and (2) to rid one’s body or a part of one’s body of toxins and other impurities. Definition two, which comes from alternative medicine, is a literalization of the spiritual sense of cleanse. The first definition is often an overpolite euphemism for genocide, but we won’t go into that decorum issue here.
Examples
For example, clean is literal in each of these sentences:
Pandora emerged from the incident covered in a tar-like substance, and spent part of the afternoon trying to clean herself. [Fairbanks Daily News-Miner]
Dany wins, and Drogo won’t get a septic infection today because the woman will clean his wound. [Wall Street Journal]
Two of the most prominent marble graves in historic East Cemetery have been cleaned of the lichens, moss, mold and mildew soiling them for decades … [Waterbury Republican American]
And cleanse is usually figurative:
It takes all of his cunning to pull off a scam that will free him from their clutches and give Lujan an opportunity to cleanse herself of the demons tormenting her. [Movie City News]
… the suggestion that this type of rehab could cleanse him of his sins is disingenuous, at best. [thedailystar.com]
But this is a town full of skeptics, people who buy into all that bricks-and-mortar-and-white-goods fandango instead of having their chakras cleansed. [NPR]

