Wood played professionally on trombone from the late 1930s. He worked with Tiny Bradshaw and Lionel Hampton in the 1940s before joining the Navy during World War II. While there he played in a band with Clark Terry, Willie Smith, and Gerald Wilson. After his service ended he returned to play with Hampton, then worked with Arnett Cobb (1947–48), Erskine Hawkins (1948-50), and Count Basie (1951).
He spent a few years outside music, then played with Duke Ellington in 1959-60 and again in 1963; he returned once more early in the 1970s. He again played with the Count Basie Orchestra from 1979 into the middle of the following decade.