His original last name was Büschel. His family emigrated to Palestine in 1933, where he started violin lessons in 1936. From 1942 until 1946, Orgrad studied violin and composing with Rudolf Bergmann and Paul Ben-Haim in Tel Aviv and in 1947 with Josef Tal in Jerusalem. In the years 1949, 1952, and 1961 he took part in composing courses at the Berkshire Music Center in Tanglewood, with Aaron Copland and others. From 1960 until 1962 he studied composing at Brandeis University in Waltham.
Beginning in 1956, Orgad was employed by the Israeli Ministry of Education, in the department of its school of music. His musical works consist primarily of choir music and songs, although he also wrote orchestral works and chamber music.