I heard someone describe another person as having a 'disturbed and sick mind.'Please give us the complete sentence in which you found, or would use, the phrase, along with some context.
A 'disturbed and sick mind' is the sort of thing people say when they mean to suggest that a person may have a mental disorder. It is highly subjective. I suppose that all it usually means is that the speaker has very different opinions from the person they're talking about. There are many politicians these days who some people think have mental disorders, but whose views other people support.
All depends on who is speaking and who they're speaking about.