He was born at the Republic of Venice, and began the study of rabbinical literature at an early age. When thirteen years old, he became the pupil of David Franco. From him Aboab received the intellectual tendency which he followed all his life. When eighteen years of age, he married the portionless daughter of Franco, named Mazzal-Ṭob, a proceeding unusual at that time.
He was first appointed rabbi in Verona, whither his father and brothers soon followed him. Here he gained such a reputation for learning that disciples sought him out, and the rabbis of Italy turned to him with difficult religious questions. He became known by the name RaSHA, a word formed from the initial letters of his Hebrew name. Aboab was not only learned in all Jewish science, but also acquainted with secular learning and a master of several languages. He understood Latin and German, spoke Italian, and read and wrote Spanish. He was rigid, even ascetic, in his piety; fasted much, studied the Law day and night, and ate no meat on week-days. He was extremely modest and charitable, supported his disciples, and visited the poor in their dwellings.
In 1650 he was called to Venice as rabbi. There he became involved in the controversy concerning Shabbethai Ẓebi and his representative or apostle, Nathan of Gaza. The latter confessed to Aboab, as president of the rabbinical tribunal (bet din) of Venice, that his (Nathan of Gaza's) prophecies concerning the Messianic character of Shabbethai Ẓebi were mere deceptions.
In advanced age Aboab became the victim of many misfortunes. Domestic troubles and severe illness afflicted him, and in his eightieth year he was compelled to leave Venice and his family, and to wander from place to place. It was only shortly before his death that he received permission from the doge and the senate of Venice to return to the city and to reassume his office, which in his absence had been conducted by his son Joseph. Before his death he called together his four sons, Abraham, David, Jacob, and Joseph, and besought them never to pronounce carelessly the name of God, to be scrupulously honest in all their dealings, never to calumniate, never to give any one a contemptuous appellation or nickname, but to care for the education of the young, and to attend synagogue daily. He died in Venice.
Of his works there have appeared: "Debar Shemuel" (Word of Samuel), a collection of rabbinical decisions (Venice, 1702); and, anonymously, "Sefer ha-Zikronot," a treatise on ethical conduct (Venice, 1650). Rabbi Joshua ben David, of Venice, composed an elegy upon his death, printed in the collection of poems "Kos Tanḥumim" (Venice, 1707).