Maxwell was born in Arbroath and began his career as an amateur playing for Hearts Strollers, Arbroath, Heart of Midlothian and Dundee whilst working as a solicitor's clerk. He was persuaded by Stoke manager Bill Rowley to become professional and he did so joining the Potters in the summer of 1895. Maxwell scored on his Stoke debut on the opening day of the 1895–96 season, in a 2–0 win over Bolton Wanderers. He initially had to bide his time as fellow Scottish forwards Billy Dickson and Tommy Hyslop were established in the first team. Following the departure of both Dickson and Hyslop in the summer of 1896 Maxwell became Stoke's main attacking threat and he became the clubs first prolific goalscorer. He finished up as top goalscorer for five seasons in a row, hitting 16 in 1896–97, 11 in 1897–98, 19 in 1898–99, 11 in 1899–1900 and 16 in 1900–01. Maxwell was not a typical 1890s inside-forward as most relied on strength and power, Maxwell used his pace to sprint away from defenders and most of his goals came in one-on-one situations with the goalkeeper. Maxwell helped Stoke reach their first FA Cup semi-final in 1899 where he scored Stoke's only goal in a 3–1 defeat against Derby County. Maxwell was renowned for his gentlemanly conduct on the pitch but on one occasion playing against West Bromwich Albion in October 1899 he lost his temper with Albion's Abraham Jones and the pair traded blows and were both sent-off. Maxwell received a two-week suspension during with time he played in a benefit match for Sheffield United's Arthur Watson. He suffered a serious knee injury in that match and missed a further ten weeks. With his injury Stoke decided to cash in on him, selling him to Third Lanark for £250, which turned out to be poor business as Stoke failed to find a suitable replacement and later suffered heavy financial problems. After a season back in Scotland he moved to Sunderland and then to Millwall Athletic where he scored 34 goals in 54 Southern League games. His final move of his career took him to Bristol City where he enjoyed great success, scoring 27 goals in 1905–06 as the Robins won the Second Division title. He then hit 19 goals in 1906–07 as they nearly won the First Division title missing out by three points to Newcastle United. Maxwell retired in 1909 and decided to move to Belgium to take up a coaching role with the Belgium national team.
Cricket career
Outside of football, Maxwell played a single cricket match for Staffordshire in the 1904 Minor Counties Championship against Dorset. In Staffordshires' first innings, he was dismissed for 4 runs by Hubert Greenhill, becoming one of Greenhill's 8 victims in the innings. In their second innings, he opened the batting, scoring 18 unbeaten runs.
