I don't know if this is the same man, but it sounds likely. I am not related and am not researching this family. From the booklet "Historical Atlas of Westmoreland County, Virginia" by Davie Eaton, 1942:
"Joesph Murdock was from King George County and owned a mill just above the Bristol Mines Run. He bought this mill from John Jett, Jan. 19, 1762. He made his will Oct. 11, 1769, proved Mars. 1, 1770, in which he leaves the mill to a son, William. His widow, Mary Murdock was assessed in 1782 with 23 slaves in King George County."