It condemned "the misogynist, hateful comments" it said had been made by Mr Trump about women and minorities.
It follows the release of a 2005 video last week in which Mr Trump makes remarks about groping women.
Mr Trump has apologised for remarks, which he described as as "locker-room talk".
He has also denied touching women inappropriately.
The motion was filed by Greens party MP Jeremy Buckingham to the Upper House of the NSW parliament.
It said: "This house... agrees with those who have described Mr Trump as a 'revolting slug'."