Greenspan was born in the village of Lyakhovichi in the Minsk Governorate of the Russian Empire, where his father Yaakov Moshe was engaged in commerce. There he gained a reputation for his vast Talmudic knowledge and expertise while still in early youth. He studied under the greatest rabbis of his generation, including such legendary figures as the Sfas Emes, Rabbi Meir Simcha of Dvinsk and the Ridvaz, as well as learning under and with the Avnei Nezer; Rabbi Chaim Soloveitchik; the Rogatchover Gaon; the Chofetz Chaim; and Rabbi Aharon Kotler, all world-renowned rabbinic luminaries. Rabbi Greenspan obtained semicha at the young age of eighteen, indicative of his acceptance into the highest circles of rabbinic scholarship due to his tremendous knowledge and ability.
Upon the outbreak of World War I, Rabbi Greenspan fled to Britain via Belgium with his children. His wife Beila returned to Warsaw to look after the family's restaurant business. Initially he was Rosh Yeshiva in Liverpool and later moved to Leeds to take up the position of Rosh Yeshiva there. He finally moved to the East End of London, where he assumed leadership of the Etz Chaim yeshiva. Rabbi Greenspan remained at Etz Chaim for the rest of his life, where he produced many hundreds of learned students and pupils alongside distinguished colleagues such as Rabbis Elya Lopian, Leib Gurwicz and Nosson Ordman. Among his more well-known students were future Chief RabbiLord Jakobovits, Dayan Pinchas Toledano, Judge Leonard Gerber and Arnold J. Cohen. Rabbi Greenspan died at the age of eighty-three, and with his death Europe lost one of its primary and most exceptional Torah scholars. A large number of people attended his funeral, where he was eulogised by Chief Rabbi Israel Brodie, Rabbi Leib Gurwicz, Dayan Grosnass of the London Beth Din and Rabbi Eliezer Lopian, rosh yeshiva of Toras Emes in London. Rabbi Greenspan met Rav Kook when he just came to Britain and became his talmid. Writing of Rabbi Greenspan in the Jewish Chronicle, Rabbi Nosson Ordman described his deceased colleague as the "humblest and most well-mannered of men" despite his "scholarship and intellectual" abilities. He noted that Rabbi Greenspan's death was "a great and irreplaceable loss both to the yeshiva and Anglo-Jewry. He was... one of the outstanding... Talmudists of this generation". Rabbi Jakobovits, in deep reverence of Rabbi Greenspan, commented, "he may have been the greatest Torah scholar in England" and also noted his teacher's great modesty and knowledge of secular disciplines. Rabbi Greenspan was survived by his wife, two daughters, son and grandchildren. Although he left many Halachic and Talmudic writings, a large number of his written manuscripts were destroyed in the First World War.
