Born in Dumbarton, Duncan was working as a law clerk when he joined his home-town club Dumbarton in 1906. He moved to Newcastle United in March 1908 for a fee of £150. A versatile forward, although primarily an outside-right, he scored 12 times in 81 league games for the Magpies and was a member of the 1908–09Football League championship winning side.
In May 1913, he returned to Scotland, moving to Rangers for a fee of £500. He remained with Rangers during World War I, in which he served as a signalling instructor in the Royal Field Artillery. He also played two wartime games for Celtic. In 1918 he rejoined Dumbarton and in the 1920 close season signed for Cowdenbeath. In 1922 he rejoined Dumbarton for a third time, but retired at the end of the 1922–23 season.
Scott Duncan was appointed as secretary-manager of Hamilton Academical in the summer of 1923. He left in October 1925 to take over as secretary-manager of Cowdenbeath and had seven successful years at the club, keeping them in the Scottish First Division throughout his time in charge.
In June 1932 he was appointed as secretary-manager of Manchester United. Despite spending a lot of money on players, United were almost relegated to the Third Division in the 1933–34 season. However, Duncan turned things around and lead United to the Second Division championship in the 1935–36 season. However, they were relegated the following season and, in November 1937, he resigned to become manager of Ipswich Town, who were then a Southern League side.
At the end of the 1938–39 season Ipswich were elected into the Football League despite finishing third in the Southern League. Scott Duncan remained with Ipswich Town as manager for 18 years, winning the Third Division (South) title in the 1953–54 season. However, Town were relegated the following season and Duncan stood down as manager in August 1955 season when Alf Ramsey took over. He remained as secretary for three further years.