Gutnick was born in Zolotonosha, Ukraine; soon afterwards his family moved to Tel Aviv, and then in 1927 to London, where his father, Mordechai Ze'ev Gutnick, a graduate of the Tomchei Temimim yeshiva, served as a Chabad rabbi. After his father's death, on 29 November 1931, Gutnick came under the influence of Yehezkel Abramsky. He was educated at the Jews' Free School in London, and then at the Telshe yeshiva in Lithuania. When the Second World War broke out, he escaped with a small group of refugees, including the wife and daughter of Eliyahu Eliezer Dessler, which eventually found its way to Australia in 1941. On the instruction of the Rebbe of Lubavitch, Rabbi Joseph Isaac Schneersohn he remained in Australia, and joined the Australian Army. He applied for a position as a chaplain, but was turned down.
After the war Gutnick's stepfather Osher Abramson accepted a rabbinic position in Sydney, Australia, and moved there together with Gutnick's mother and his brother, Sholom Gutnick. Gutnick married Rose Chester, and had six children together. Their son Joseph is a well-known Jewish philanthropist; their son Mordechai is a prominent Orthodox Jewish rabbi in Australia. Gutnick's grandson, Moshe Hecht, is a singer/songwriter and is the lead singer of the Jewish folk rock group Moshe Hecht Band.
In 1967, Gutnick founded the Rabbinical Council of Victoria, and served as its president until his death. He was also honorary Rosh Yeshiva at the Rabbinical College of Australia and New Zealand, where he delivered a monthly lecture and examined the students.
- Speech by Steve Bracks on 19 November 2000, at a JNF dinner in Gutnick's honour.
- "Man's steps are ordained by God, and since Providence has guided you to Australia, this is your place [...] Prepare the ground for the arrival [of Jewish refugees] so that it will be a place of Torah, where God can be found."
- Speech by Rabbi Gutnick on 20 April 2003, at Kollel Beth Hatalmud.
- Elwood Talmud Torah Hebrew Congregation, by Yossi Aron
- Dan Goldberg (2003-10-31). "Obituary". Australian Jewish News.
- Malcolm J Turnbull. "Safe Haven: Records of the Jewish Experience in Australia".