Though his family originally lived in Hamburg, Germany, Jacob and his brother were both born in Spain. At some point in time, his family moved to Amsterdam where he studied at the De los Pintos rabbinical academy in Rotterdam. In 1655 he was appointed hakham of that city. On May 3, 1655, Abendana delivered a famous memorial sermon on the Cordovan martyrs Marranos Nunez and Almeyda Bernal who had been burned at the stake.
Several years later, with his brother, Isaac, Jacob published the Bible commentary Miklal Yofi by Solomon ben Melekh which included his own commentary, Lekket Shikchah (Gleanings), on the Pentateuch, the Book of Joshua, and part of the Book of Judges. This was published by subscription in Amsterdam in 1660 with a second edition in 1685.
Having gone to Leyden seeking subscribers, Jacob met Anton Hulsius with whom he helped in his studies. Hulsius tried to convert Jacob to Christianity which began a life long correspondence between the two. The Abendana brothers similarly impressed other Christian scholars, such as Johann Buxtorf (Basel), Johann Coccejus (Leyden), and Jacob Golius (Leyden).
With Hulsius, Jacob entered into a polemical discussion of the verse in the Book of Haggai: "The latter splendor of this house shall be greater than the former" (2:9), which Hulsius attempted to prove was a reference to the Church. The debate lasted via correspondence from September 24, 1659 to June 16, 1660. Abendana responded with a Spanish translation of Rabbi Judah Halevi's Kuzari in 1663. Hulsius eventually published the correspondence between the two in 1669.
In 1675, Jacob addressed the community at the dedication of the new synagogue in Amsterdam. Five years later, in 1680, he was brought to London to succeed Joshua da Silva as Hakham of London where he served for 15 years as the hakham of the Spanish and Portuguese Synagogue in London. Over the following years, he completed a Spanish-language translation of the Mishnah, along with the commentaries of Maimonides and Obadiah of Bertinoro. The work was frequently cited by Christian theologians, though it was never published. Jacob Abendana died childless in London in 1695 and was buried in the Portuguese cemetery at Mile End.
Abendana, Jacob in The Jewish encyclopedia : a descriptive record of the history, religion, literature, and customs of the Jewish people from the earliest times to the present day'', New York ; London : Funk & Wagnalls Company, 1901-06, volume 1, p 53.