Passed Midshipman, Wyman spent a tour of duty ashore at the Naval Observatory, Washington, D.C., before reporting to the receiving ship Franklin at Boston, Massachusetts, and subsequently being promoted to lieutenant on 16 July 1850.

Commanding the steamer Pawnee from October 1861, Wyman took part in Flag Officer DuPont's capture of the key seaport of Port Royal, South Carolina.

Transferred to the West Indian Squadron the following October, he commanded the steam sloop Wachusett and the paddle steamer Santiago de Cuba, and captured the blockade runners Britannia and Lizzie.

After that tour of sea duty, Wyman headed the Navy's Hydrographic Office for eight years, receiving promotions to commodore on July 19, 1872,[2] and to rear admiral on April 26, 1878.

Under Wyman's direction, the office began a systematic and sustained program of worldwide charting and surveying, the precursor of the navy's present globe-girdling oceanographic research effort.