Mizrachi was born in Constantinople; he was a Romaniote Jew, meaning that his family was local Greek-speaking, and not from the Spanish exile.
As a young man, he distinguished himself as a Talmudist, yet he also studied the secular sciences, particularly mathematics and astronomy; he is said to have been the first to derive a method for the extraction of the cube root.
Mizrachi succeeded Moses Capsali (on his death c. 1495) as Hakham Bashi "Grand Rabbi" of the Ottoman empire; he held this position for the rest of his life.
A compendium by Jacob Marcaria was published under the title Kitzur Mizrachi (Trento, 1561), and later, one by Isaac ha-Kohen of Ostroh, entitled Mattenat 'Ani (Prague, 1604-9).
Several commentaries have been written on Mizrachi, including Yeri'ot Shlomo by Solomon Luria (Maharshal), a supercommentary on Sefer ha-Mizrachi by Barzillai ben Baruch Jabez, and strictures on the work by Samuel Edels, (Maharsha).