Roth was born on June 13, 1948 to Frances and Lawrence Roth. He grew up in New Hyde Park, Long Island, New York. In 1959, Roth's father volunteered his Joe and his brother Daniel to be plaintiffs in a case against the New York State Board of Regents, as part of the ACLU's nationwide effort to abolish mandatory prayer in public schools. The case went through several appeals, finally reaching the U.S. Supreme Court in 1962. The Court ruled that such prayer was unconstitutional under the First Amendment, in the landmark case of Engel v. Vitale. Roth has stated that his Jewish family faced various forms of harassment. This involved incidents like "a cross being burned on the lawn and some of Roth's schoolmates crossed themselves before they would speak to him."
Roth attended Boston University, graduating in 1970 with a bachelor's degree in communication.