Born in Everett, Massachusetts, Smith was raised in Miami, graduating in 1954 from Miami Senior High School where he played football and became a High School All American. He transferred from Brandeis University to Florida State University on a football scholarship graduating in 1959 with a B.S. degree in Philosophy.
Smith was of Jewish religion. He briefly attended Brandeis University, where he met and married his first wife, Norma Kalman. They had one son, Elliot. Paul and Norma were divorced in 1960. Smith married Eve Smith. In February 2006, they immigrated to Israel, adopting Ra'anana as their new home. After taking Israeli citizenship, the couple adopted Hebrew names: Adam and Aviva Eden.
In 1977, Smith moved to Hollywood, making appearances in such films as 21 Hours at Munich (1976), Midnight Express (1978), as Bluto in Popeye (1980), and as Glossu Rabban in Dune (1984).
On April 25, 2012, Smith died in Ra'anana. The cause of death is unconfirmed.
