He was born at Torpoint, Cornwall, United Kingdom, educated at Kelly College, Devon, and left for New Zealand in 1921 where he studied architecture for four years. In 1926 he joined the New Zealand Free Lance as cartoonist, but soon transferred to the Christchurch Sun and thence to the Auckland Sun. He joined the New Zealand Herald as a political cartoonist in 1930 and although he officially retired in 1976, contributed cartoons to the newspaper for more than another decade.
Grant (1987) describes Minhinnick as "pre-eminent among New Zealand cartoonists. His work for the country's largest newspaper was widely syndicated and of a consistently high standard; witty rather than barbed, and with a feel for caricature that gave the cartoons an added dimension". Minhinnick was strongly influenced by New Zealand cartoonist David Low, and was offered, but declined, Low's job at the London Evening Standard when Low left the London newspaper in 1949. Minhinnick also taught Les Gibbard (the cartoonist who went on to replace Bill Papas, Low's successor, then at The Guardian) in Auckland during the 1950s.
Minhinnick illustrated several popular New Zealand books ("Murphy's Moa", "From N to Z", "Trout at Taupo", "Four Seasons of Country Diary" ), and he regularly published collections of his work (such as "The Minhinnick annual", "Min's Sauce"  to "Just a Min" ).
- "No. 38931". The London Gazette (Supplement). 8 June 1950. p. 2814.
- "No. 46921". The London Gazette (Supplement). 4 June 1976. p. 8055.
- Grant, Ian: "The Unauthorized Version - A Cartoon History of New Zealand 1840-1987", 2nd ed., pages 134-135. David Bateman Ltd, 1987. ISBN 0-908610-72-6
- Pat Lawlor: "Murphy’s moa and other Xmas sketches", illustrated by Gordon Minhinnick and Fred Alexander, Simpson & Williams - Christchurch, N.Z., 1936.
- C.V. Smith: "From N to Z - a humorous survey of New Zealand", illustrated by G.E. Minhinnick, Hicks Smith & Wright, 1947.
- O.S. Hintz: "Trout at Taupo", illustrated by G.E. Minhinnick, Max Reinhardt - London, 1964.
- E.V. Sale: "Four seasons of Country Diary", illustrated by Sir Gordon Minhinnick, Reed - Wellington, N.Z., 1982. ISBN 0-589-01401-3
- G.E. Minhinnick: "The Minhinnick annual : a selection of cartoons from the New Zealand herald and the Auckland weekly news, by Minhinnick", Wilson & Horton - Auckland, N.Z., 1933.
- G.E. Minhinnick: "Min’s sauce : cartoons from the N.Z. Herald 1970-1976, by Minhinnick", Wilson & Horton - Auckland, N.Z., 1976.
- G.E. Minhinnick: "Just a Min : cartoons from the New Zealand herald, by Minhinnick", Wilson & Horton - Auckland, N.Z., 1983. ISBN 0-86864-065-4