Stepovy was born Yakiv Yakymenko (Akimenko) in Kharkiv, in the Russian Empire (in present-day Ukraine). Stepovy's older brother, Theodore Akimenko), was also a composer. Stepovy was a representative of the Ukrainian musical intelligentsia of the 20th century. He was one of the founders of the national school of composition and composed in the tradition of Mykola Lysenko.
During World War I, Stepovy was recruited to the military, where he worked as a secretary on a hospital train. He served in the military for almost three years, until he managed to get released in April 1917. After this he settled in Kiev where he worked as a teacher at the Kiev Conservatory and a musical critic.