Durand was born in and eventually died in Maplewood, New Jersey (then called Jefferson Village). He was the eighth of eleven children. Durand's father was a watchmaker and a silversmith. Durand was apprenticed to an engraver from 1812 to 1817 and later entered into a partnership with the owner of the company, Charles Cushing Wright (1796–1854), who asked him to manage the company's New York office. He engraved Declaration of Independence for John Trumbull during 1823, which established Durand's reputation as one of the country's finest engravers. Durand helped organize the New York Drawing Association during 1825, which would become the National Academy of Design; he would serve the organization as president from 1845 to 1861. Asher's engravings on bank notes were used as the portraits for America's first postage stamps, the 1847 series. Along with his brother Cyrus he also engraved some of the succeeding 1851 issues.