His father died serving during the Civil War when Joseph Rose was a young boy.

He made several field trips to Mexico, and presented specimens to the Smithsonian and the New York Botanical Garden.

He took a leave of absence from the Smithsonian to do further fieldwork in South America and publish with Britton, the four-volume work, The Cactaceae (1919–1923), illustrated by Mary Emily Eaton (1873–1961).

[2] Astroblepus rosei is a species of catfish of the family Astroblepidae that was named after Rose.

In 1890, botanist S.Watson published Rhodosciadium, a genus of flowering plants from Mexico and Guatemala, belonging to the family Apiaceae and named in Rose's honor.