Born in Petah Tikva during the Mandate era, Tzipori attended a religious school in his hometown. In 1939 he joined the Irgun, and in 1945 was arrested by the British authorities and exiled to Africa, where he was interned in British detention camps in Eritrea, Kenya and Sudan. Also he managed to escape from a detention camp in Eritrea, but was caught.
He was sent back to Israel after its independence in 1948, and became a professional soldier, serving in the IDF from 1948 until 1976. He completed an officer's course in 1950, graduated from the IDF Command and Staff College in 1959, and studied at Tel Aviv University.
Between 1962 and 1965 he was an Armoured Battalion commander, becoming commander of the Armor School in 1968 and deputy commander of the Armor Corps in 1971. In 1973 he was appointed Commander of Command and Staff, becoming Deputy Head of Operations in the General Staff in 1974. He was demobilised in 1976 with the rank of Lieutenant General.
The following year he was elected to the Knesset on Likud's list, and in June 1977 was appointed Deputy Minister of Defense. Following the 1981 elections he became Minister of Communications, also briefly serving as Deputy Defense Minister between August 1981 and October 1983. He lost his seat and place in the cabinet in the 1984 elections.