George Bissell was born in New Preston, Connecticut, the son of a quarryman and marble-cutter. During the American Civil War he served as a private in the 23rd Connecticut Volunteers in the Department of the Gulf (1862-1863), and on being mustered out became acting assistant paymaster in the South Atlantic Squadron. At the close of the war he joined his father's marble business in Poughkeepsie, New York.
He studied the art of sculpture abroad in 1875-1876, and lived much in Paris during the years 1883-1896, with occasional visits to America. Among his more important works are:
• Union Soldier, Town Green, Colchester, Connecticut, 1875.
• Frederic de Peyster, New York Historical Society, New York City, ca. 1875.
• Chatfield Monument, Riverside Cemetery, Waterbury, Connecticut, ca. 1880.
• Soldiers' Monument, The Green, Waterbury, Connecticut, 1882-85.
• General Horatio Gates, Saratoga Battle Monument, Saratoga, New York, 1885-86.
• Soldiers' Monument, Soldiers' Monument Park, Winsted, Connecticut, 1887-90.
• Sam Sloan, Lackawanna Ferry Terminal, Hoboken, New Jersey, 1889.
• Chancellor John Watts, Trinity Churchyard, New York City, 1890.
• Columbia, atop Soldiers' Monument, Civil War Memorial Park, Salisbury, Connecticut, 1891.
• Bas-relief panel of Robert Burns and Highland Mary, pedestal of G. A. Lawson's Statue of Robert Burns, Ayr, Scotland, 1891.
• Lincoln Memorial (In Memory of Scottish-American Soldiers), Old Carlton Burying Ground, Edinburgh, Scotland, 1893.
• Colonel Abraham de Peyster, New York Historical Society, 1896. This statue stood in Bowling Green Park from 1896 to 1972, and in Hanover Square from 1976 to 2004.
• Chester A. Arthur, Madison Square, New York City, 1898-99.
• Chancellor James Kent, Library of Congress, Washington, D.C., ca. 1899.
• Bust of Admiral John A. B. Dahlgren, Smith Memorial Arch, Fairmount Park, Philadelphia, Pennsylvania, 1901-04.
• Abraham Lincoln, Lincoln Park, Clermont, Iowa, 1902. A replica of Bissell's statue in Edinburgh, Scotland.
Bissell also created smaller works, such as a bust of President Abraham Lincoln as well as a larger statue of the president.