The same way.
Or if you wanted to disambiguate, you could also say, "Ist das Wasser da schmutzig?", with "das ... da" for explicit "that" as opposed to "the".
In speech, "Ist das Wasser schmútzig?" ("the") / "Ist dás Wasser schmutzig?" ("that") would generally be clear enough -- the words meaning "that" are stressed in speaking while the words meaning "the" are usually not.
I feel like in English "unclean" and "dirty" mean the same thing technically but in usage they mean different things. When I hear "unclean" it's typically in religious settings such as certain foods or acts are unclean or the idea of something being spoiled. I think "unclean" usually applies to the spiritual or emotional whereas dirty is a little different. But that may just be what I hear the most.
Can "schmutzig" be used to describe people?
If they have been working in the garden and are physically dirty, yes. Wasch dir vor dem Essen bitte deine schmutzigen Hände! "Wash your dirty hands before the meal!"
Can it also mean "dirty" as in "dirty thoughts"?
Yes -- and in this case, it's metaphorical, as in English. For example, schmutzige Gedanken might be thoughts about adultery.
We use it in "schmutzige Gedanken" (obscene thoughts), but we don't use it anymore for people (you may find it in older books). Also a bit old fashioned is "schmutziger Film" (sexually explicit movie). Today it is just a "Porno" in German. She is a dirty girl - "sie ist ein freizügiges Mädchen" oder "ein unanständiges Mädchen". "Du bist ein unanständiges Mädchen" today sounds more funny, like you're joking.