Tzipori became a member of Irgun in 1939. From 1945 to 1948 the British detained him in Africa.
In the 1960s Tzipori was commanding an armoured battalion, and later on the armor school. In 1971 he became deputy commander of the Armor Corps, in 1973 commander of Command and Staff, and in 1974 deputy head of operations in the general staff. In 1976 he left the army as a lieutenant general.
He entered the Knesset in 1977. From 1977 to 1981 he served also as deputy defense minister in the First and Second Begin Government, and from 1981 to 1984 also as communications minister in the Second Begin Government and the First Shamir Government. In 1984 he left politics.
Afterwards he was leading the National Insurance Institution.