Cutting was born in Clapham, London, and educated at Kingston Technical School. He began his engineering career aged 15 as a draughtsman with the KLG spark plug company, gaining early practical experience before moving into automotive design.
In 1946 Cutting joined the Allard Motor Company, where he designed his first complete car, establishing himself as a draughtsman and designer capable of working across the full scope of a racing vehicle.
Cutting joined Aston Martin in 1949. He participated in the DB2 redesign and worked alongside Eberan von Eberhorst on the DB3, DB3S, and DP Lagonda V12 projects. In 1955 he became Chief Designer for racing cars, a role that produced his most celebrated work.
The DBR1 — the car he designed in its entirety, including the body, engine, chassis, and suspension — won the 24 Hours of Le Mans in 1959 and is regarded as one of the greatest British racing cars of the era. Cutting also produced the DBR2 and DBR3 sports racing cars, and the DBR4 and DBR5, Aston Martin's entries into Formula One competition.
In 1961 he became Chief Designer for the company, working alongside Chief Engineer Tadek Marek and Technical Director Harold Beech under team manager John Wyer and ultimately owner David Brown. From 1962 his Project racing cars — the DP212, DP214, and DP215 — were conceived as prototype endurance racers intended to generate maximum publicity. The DP215 recorded 319.6 km/h (198.6 mph) on the Mulsanne Straight during practice at Le Mans, making it the fastest six-cylinder, front-engined Aston Martin ever built.
After leaving Aston Martin in the early 1960s, Cutting joined the Glacier Bearing Company, where he designed large bearings for steam turbines and was named on company patents.
In 1966 he joined the Ford Motor Company as a race car design engineer. He initially worked on the GT40 racing project with John Wyer at Advanced Vehicles in Slough, before circumstances redirected him to Ford of Britain's advanced chassis engineering division. There he contributed to the early stages of the Ford Capri project and worked through advanced pre-production on subsequent models up to the Ford Granada. In the latter stages of his Ford career he engaged with European governments and the Common Market on the development of international motor vehicle construction law. He remained with Ford until his retirement in 1985.
During retirement Cutting was engaged as a consultant on technical and legal matters, including an advisory return to Aston Martin where he assisted Victor Gauntlett on several projects. He was an associate member of the British Racing Drivers Club and a full Fellow of the Institution of Mechanical Engineers, and gave lectures and wrote technical papers throughout his post-retirement years.
In 2008, Stuart Bailey and Brian Joscelyne — both active members of the Aston Martin Owners Club — persuaded Cutting to record his story in audio. The transcribed recordings formed the basis of a 268-page book, Cutting Edge Conversations, which included a DVD of a full Institution of Mechanical Engineers lecture on Racing Astons he delivered in 2003. The limited-edition volume was published with Cutting's full consent shortly before his death and is exclusive to the Aston Martin Heritage Trust.
Ted Cutting occupies a singular place in British motorsport engineering. The DBR1 he designed in every detail secured Aston Martin's only Le Mans outright victory and remains a benchmark of 1950s sports car construction. His span of work — from hand-crafted Allard racers through championship sports prototypes, Formula One cars, and the Mulsanne-record DP215 — represents the breadth of engineering ambition that characterised British motorsport's formative decades.