Yassky was born in Kishinev, Russia. While studying medicine at the University of Odessa, he became active in the Zionist movement. Before World War I he took part in Jewish self-defense against pogromists in Odessa.
In 1920, Yassky immigrated with his wife Fanny (maiden name Gorodetsky) whom he married in Odessa; to Palestine, where he was appointed district physician of Haifa. As an ophthalmologist, he initiated programs to eradicate trachoma. In 1931, Yassky became director of the Hadassah Medical Organization. He was one of the driving spirits behind the establishment of the Rothschild-Hadassah University Hospital on Mount Scopus, which was opened in 1939.
Yassky was killed in the Hadassah medical convoy massacre during the 1948 Arab-Israeli war, approximately one month before Israel's declaration of independence. A bullet went through his liver and he exsanguinated in about ten minutes.