Alex Wood was born January 15, 1911 in Falkirk, Scotland. He was a free agent signing by the Chicago Black Hawks in the summer of 1930 who made his debut in the National Hockey League some seven years later.
A member of the Regina Pats of the Southern Saskatchewan Junior Hockey League that reached the Memorial Cup in 1929, Wood skated for the Ottawa Edinburghs of the Ottawa City Hockey League and the Regina Aces of the Southern Saskatchewan Junior Hockey League before joining the International Hockey League's Cleveland Indians in 1930-31.
Following a two-year stay with Indians, Wood joined the Canadian American Hockey League where he had stops in Boston, Quebec, Philadelphia, and Providence before returning to the International Hockey League for the 1935-36 season.
The Rochester Americans of the IHL was the next stop for Wood. It was a short stay, however, as he spent the majority of the 1935-36 season with the Buffalo Bisons of the IAHL. A First Team IHL All-Star in 1936, Wood signed as a free agent with the Cleveland Barons of the IAHL early into the 1936-37 season after the Bisons folded. Released by Cleveland after only three games, Wood signed with the New York Americans and was assigned to the New Haven Eagles before making his only National Hockey League start with the Americans in January 1937.
From 1937 to 1940, Wood was a member of the Minneapolis Millers of the American Hockey Association where he was a First Team All-Star in 1938 and 1941 before joining the AHA's St. Louis Flyers for the 1940-41 and 1941-42 seasons. After being named an AHA Second Team All-Star in 1942, Wood began the 1942-43 season with the IAHL's New Haven Eagles before being traded to Chicago.
Twenty-one games into the 1942-43 season, Wood joined the Hull Volants of the Ottawa City Hockey League (1942-44)/Quebec Senior Hockey League (1944-45) where he played the last three years of his career.