David Macleish Smith was born in Elgin, Scotland, in 1900. He was educated at Blairgowrie High School and the University of Glasgow, Scotland, graduating in 1920 with a BSc (Engineering). The University of Glasgow also awarded him a DSc in 1932 for his thesis on the motion of a rotor carried by a flexible shaft in flexible bearings, and an honorary LLD in 1967. During the First World War, Smith served as a private in the Gordon Highlanders, returning to his studies at Glasgow University when he was demobbed in 1919.

His working career began in 1920 when he went to Manchester, England, as an apprentice to Metropolitan-Vickers Electrical Company Ltd (Metro-Vicks). He remained with the company until he retired in 1966. At Metro-Vicks, he was a member of the team which carried out pioneering work in the development of the first British axial flow jet engine for aircraft.

He became a Member of the Institution of Mechanical Engineers (MIMechE) in 1938 and a Fellow of the Royal Aeronautical Society (FRAeS) in 1949. He was awarded the Silver Medal of the Royal Aeronautical Society and was a founder Fellow of the Fellowship of Engineering.