Yosef was born on May 5, 1917 in Turkey to his parents Yitzhak and Sembel. He finished studying in the Italian school in Istanbul. In the 1930s, a Beitar chapter was organized, and Yosef joined it. In 1935, he made aliyah, joining the Beitar company in Herzliya. They were active supporters of the idea of Hebrew labor, i.e. hiring Jews to work in the orchards. A Jewish orchard owner complained to the police about the violence they committed, and they were arrested, tried and sentenced to six months in prison at Nur Shams. Yosef was among them.
The Beitar company commander recommended that he be recruited for IZL, and he was trained and assigned to guard duty. He also was responsible for maintaining firearms and even helping Mapilim who had reached the shore.
Yosef took part in many anti-British activities, and this included operations such as blowing up a government communications hub. He later said that this was the only occasion on which he ever smoked a cigarette — in order to light the fuse.
Another operation involved bombing an Arab café by Rushmiyeh Bridge, where British soldiers used to congregate. Yosef told his commander that there were no British personnel in the café and he would not harm civilians.
Between 1938 and 1941, he studied electrical and mechanical engineering at the Technion in Haifa. After the IZL split, in 1940, he followed Yair. Yosef would personally meet with Yair and was very much influenced by him. Eventually he had to leave the operations division to help his mother, but he continued to recruit and train others in firearms. As the War of Independence began, he was in the Battle of Ramat Yohanan. After the Bernadotte assassination, Yosef hid Gera in his home. However, he himself was soon arrested as a Lehi member and sent to the military prison at Sheikh Munis in North Tel Aviv.
Yosef married Rachel BaRZaM (Bnei Rabbi Zechariah Mendel), and they had a son, two daughters and numerous grandchildren.
After being discharged, Yosef worked at the electric company, in the northern district, until 1971. He then set up his own business, Yosef Mitrani Engineering Consultants Limited. He worked in the electrification of Arab villages, kibbutzim and lookouts.
Yosef died of a heart attack on November 10,1986. He was buried in the Haifa Cemetery.