Born in 1938 in Shipley, West Yorkshire, England, Rutherford earned his bachelor's degree in 1959 and a doctoral degree in 1963 at Cambridge University. After working as a research associate at the U.K.'s Atomic Energy Authority's Culham Centre for Fusion Energy from 1963 to 1965, he came to PPPL, where he remained for the rest of his career.

Dale Meade, a former PPPL deputy director, said that in the early 1970s Rutherford - along with former directors Melvin B. Gottlieb and Harold P. Furth - was responsible for transitioning PPPL's fusion program from the stellarator concept envisioned by PPPL founder Lyman Spitzer to the tokamak design that was becoming the mainline fusion approach worldwide. Rutherford was a co-author of the influential 1973-74 U.S Atomic Energy Commission report WASH-1295 "Status and Objectives of Tokamak Systems for Fusion Research": https://fire.pppl,gov/wash_1295.pdf

He became head of theory at PPPL in 1972 and was appointed deputy associate director and deputy head of research in 1978. He became associate director and head of research in 1981, a position he held through the mid-1990s. In 1995 he co-wrote the 1995 textbook, Introduction to Plasma Physics. In addition to the textbook, he also authored or co-authored more than130 scientific papers. Rutherford was associate director of research at PPPL during "a period of enormous advances in tokamak research, especially at PPPL," said physicist and colleague Kenneth Young.

Among several honors he received, he was named a Fellow of the American Physical Society in 1976 and, in 1983, he received the U.S. Department of Energy's Ernest Orlando Lawrence Award, one of the highest honors in physics, for "outstanding contributions to the basic theory of plasma confinement, and to the toroidal fusion reactor concept." He retired from PPPL in 1995, but continued working at PPPL as a consultant with the ITER Project, where he was chair of the ITER Technical Advisory Committee for the design phase of ITER from 1992 to1998. He received Fusion Power Associates Distinguished Career Award in 1998.

After living in Princeton for decades, he moved to Exeter, New Hampshire, in 2010, where he spent the last 12 years with his wife Audrey Jones Rutherford. His wife died four days after her husband. The couple are survived by their daughters, Andrea Christine Rutherford and Julia Irvine Rutherford,and two grandchildren, Alexander McClintick and Samantha Trombly.