Born in Selkirk, McMahon started his career with Woodburn F.C. then Darlington St Augustines before relocating to Edinburgh. There he played with Leith Harp and Hibernian before a first venture to the professional game in England with Burnley. He returned to Hibs in February 1889 but found the club floundering due to the mass recruitment of their players by Celtic.
McMahon eventually followed the path of other former Hibernian favourites, such as Willie Groves, to Celtic in 1891. He played for the Glasgow team until 1903, making at least 217 appearances and scoring 171 goals. Equally adept at centre forward or inside left, he won three Scottish Cup medals, in 1892, 1899 and 1900, and four Scottish League medals, in 1893, 1894, 1896 and 1898. His first moment of glory came in the 1892 Scottish Cup Final replay, when he scored two goals in the 5-1 victory over Queen's Park. He also scored in the 1899 cup final when Celtic beat Rangers 2-0, and in the 1900 final when they beat Queen's Park 4-3. In 1892, following his cup final display, McMahon returned to professional football in England with Nottingham Forest but, after concerted efforts from the Celtic committee, returned to Glasgow without having played for the East Midlands side.
The advent of professionalism in Scotland the following year stemmed the southward drift and ensured players such as McMahon could earn sufficient remuneration for their talents by staying in their native country. McMahon played six times for Scotland between 1892 and 1902 and scored four goals in the 11-0 rout of Ireland in 1901. He also represented the Scottish League XI on eight occasions.
McMahon eventually left Celtic in 1903, joining Partick Thistle where he retired a year later. He earned several sobriquets during his playing days, such as the "prince of dribblers" and "The Duke". The later was derived from the French President Patrice de Mac-Mahon, duc de Magenta, the descendant of an Irish soldier who had severed under Napoleon. Writer John Cairney[who?] recounts that when the duc de Magenta died, Glasgow news-vendors cried "McMahon died! McMahon died!" to sell more papers. Many Glaswegians purchased the paper under the assumption that the story referred to the popular Celtic player, rather than the far-removed foreign politician.
- Lamming, Douglas (1987). A Scottish Soccer Internationalists Who's Who, 1872-1986. Hutton Press. ISBN 0-907033-47-4.
- The Football Association had legitimised professionalism in 1885; the Scottish Football Association would not follow suit until 1893.
- "Scotland FL Players by Appearances". Londonhearts.com (London Hearts Supporters' Club). Retrieved 27 November 2011.
- Cairney, John (2004). A Scottish Football Hall of Fame (Paperback). Mainstream Sport. ISBN 1-84018-920-7.