Snell was born on December 19, 1903 in Bradford, Massachusetts. He was the youngest of three children. In 1926, Snell received a Bachelor's degree from Dartmouth College. After recommendation by John Gerould, his genetics professor at Dartmouth, Snell completed graduate work at Harvard University where he worked with William E. Castle. In 1930, Snell earned his PhD from Harvard. After he earned his PhD, he worked at Brown University from 1930 to 1931. After he left, he spent two years at the University of Texas as a postdoctoral fellow. He worked with H. J. Muller, a pioneer of radiation genetics (and later, a Nobel Prize winner). Snell worked at WUSTL as a teacher from 1933 to 1934. After he had some short stints as a teacher, Snell joined the Jackson Laboratory staff in Bar Harbor, Maine and spent the rest of his life there. He died on June 6, 1996 in Bar Harbor, Maine.