Thrupp was promoted to commander on 17 September 1858, and served as commander aboard HMS Desperate in the North American Station and the West Indies, from 30 July 1862 to 7 November 1863.
By his first wife, Mary Burgon, Joseph was father of Dorothea Ann Thrupp the hymn-writer, and of John Augustus Thrupp (1785–1814), the father of John Thrupp the historian; also of Charles Joseph Thrupp, the father of Admiral Arthur Thomas Thrupp.
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