Harav Mordechai Gifter was born in 1915 in Portsmouth, Virginia, He was raised in Baltimore, Maryland, where his father owned a grocery. He attended the Baltimore City Public Schools, at the time being known as Max, and received his religious education in after-school programs.
As a young man, Rav Gifter studied in RIETS in New York City and was a Talmid of Reb Moshe Aharon Poleyeff and Reb Moshe Soloveichik.
In 1932, Rav Gifter traveled to Lithuania on the same boat as Harav Avigdor Miller to study in the Telshe Yeshiva, Where he developed a strong bond with Harav Zalman Bloch, the mashgiach at the yeshiva. He eventually became engaged to Reb Zalmens's daughter.
In 1939, prior to his wedding, Rav Gifter returned home to the United States to visit his parents in Baltimore. He planned on returning to Lithuania for his wedding and to resume his studies. When it became obvious that he would be unable to return due to the political climate of the late 1930s, Rav Gifter arranged for his Kallah's family to join him in the United States. Only his Kallah came, the family chose not to abandon their community in its time of greatest need.
Shortly thereafter, Rav Gifter was appointed Rov of the Nusach Ari Shul in northwest Baltimore. In addition to his Rabbonus, Rav Gifter was a maggid Shiur at Ner Yisroel headed by Yaakov Yitzchok Ruderman. He was the first native Baltimorean to lead a Kehilla in the city.
In 1941, Rav Gifter moved to Waterbury, Connecticut and was a Rav there. In 1944, he moved to Cleveland, Ohio to join the the newly re-established Yeshiva of Telshe, which was moved from Telshe, Lithuania to Cleveland. The original school and Telshe community were almost completely destroyed by the Nazis and Lithuanian militia.
In 1964, he was appointed as Rosh Yeshiva together with Reb Boruch Sorotzkin.
In 1977, Rav Gifter brought 20 students from Cleveland to Eretz Yisroel and opened a branch of Telz in Telz-Stone, leaving Reb Boruch in charge of the Cleveland campus. When Reb Boruch Sorotzkin was niftar in 1979, Rav Gifter was sent back to the United States to lead the Cleveland campus and the Israeli branch closed. From that point on, Rav Gifter moved into small quarters in the students' dormitory, out of distress of the Golus.