Stone was a businessman and developer who subdivided and platted what are now the Wallingford and Fremont neighborhoods of Seattle. Stone Way and Corliss Avenue in Wallingford are named after him. A Republican, he had been active in local politics for several years before being elected mayor. He was appointed to the Common Council when the Territorial Legislature chartered the city of Seattle in December 1869 and then served two terms as an elected member of the council.
John T. Jordan, Stone's predecessor, was appointed acting mayor until a special election could be arranged. Republican Moses R. Maddocks was elected to fill the final two months of Stone's term.