Words are always evolving and changing their meaning.
The word slut, like slattern, meant some on who was sloppy, untidy, didn't obey the great god cleanliness.(I suspect that slut, slattern and sloppy, probably have much the same root word behind them.) From there it is easy to suggest that a woman whose home and person is dirty and is probably disorganised, is probably as careless, dirty and disorganised in her relationships.
Now that a womans worth is no longer judged by how white her doorstep and her washing is, it is easily to see how one meaning is used less and the other meaning becomes dominant.