As a cadet, Mulzer joined the cavalry in the summer of 1914 and received a commission at the end of the year. In August 1915, he transferred to the German Air Force, serving with FFA 4b and FFA 62 before becoming a fighting pilot. He scored his first confirmed victory on 30 March 1916, shooting down a Vickers F.B.5 north of Wancourt. In July, while briefly serving with KEK B, Mulzer scored his eighth victory and became the first Bavarian to receive the Blue Max. After receiving the Knight's Cross of the Military Order of Max-Joseph, he rejoined FA 32b at Douai where he scored his final victory on 3 August 1916. The following month, Mulzer was killed in a crash while testing the performance of a new Albatros D.I.