Mücke became a naval cadet in 1900, and first served on the schoolship Charlotte, and then the battleship Kaiser Friedrich III. He became Leutnant zur See in September 1903 and was posted to the light cruiser Nymphe. He became first officer of 3rd Torpedo Boat Reserve Half-Flotilla in 1907, then flag lieutenant to Commander, Scouting Forces in 1908. He received command of the torpedo boat S.149 in 1910, while simultaneously acting as flag lieutenant for the First Torpedo Boat Flotilla.
Mücke became navigator of Emden in Autumn 1913, and her first officer in Spring 1914. At the time of the Emden's last fight, von Mücke was ashore leading a raiding party cutting the undersea cables from the station on Direction Island in the Cocos. He gathered his party and escaped in a 97-ton trading barquentine Ayesha, sailing across the Indian Ocean to the Arabian Peninsula. After many adventures some fifty Germans returned home, despite attacks by Arabs and frequent lack of cooperation from the Turks. Unfortunately for him, von Mücke attempted to expose the lack of cooperation, and was heavily criticized by German diplomats and by fellow naval officers who objected to his practice of self-promotion. He wrote and sold two books on the cruises of the Emden and the Ayesha, both published during the war. In his naval career, he he was posted to command the 15th Torpedo Boat Half-Flotilla in June 1915, then sent to command the Euphrates gunboat flotilla in January 1916. After a staff appointment back in Germany in Autumn 1916, he again commanded the Donau Half-Flotilla. Then he became navigation officer of the battlecruiser Derflinger, and finally in May 1918, became commander of the first section of the 2nd Torpedo Boat division. He was demobilized at the end of the war as a Korvettenkapitän.
von Mücke joined the National Socialist German Worker's Party but left in disgust when Hitler took it over, not liking the personality cult. Effectively a right-wing party member of a one-person party, he was left out by the Nazis, was refused permission to emigrate, and made his living on book royalties derived from his previous wartime volumes and from his subsequent authorship of coastwise navigation handbooks. The first volume of his intended political trilogy failed and the work was never completed. He died of a heart attack on 30 July 1957 at Ahrensburg, having lost a son on the Eastern Front in WWII. He was survived by his American-born wife and their four remaining children.