"We are washing the mop because it is not wet."
Translation:אנחנו שוטפים את הסמרטוט כי הוא לא רטוב.
Since I first posted the question, I've learned that zeh/zot is used more when the object hasn't already been specified, and hu/he/otoh/otah when it has. Since we specified the mop in the beginning of the sentence, we use hu at the end.
But DL does not apply that rule consistently, and it may be that modern Hebrew doesn't, either. Just yesterday I ran across a sentence similar in structure to this one, wrote hu (or maybe otoh), and was corrected to (et) zeh.