Mayer was born into a prominent Pennsylvania family. His father had a distinguished military service record and worked as a stockbroker; an uncle, Will Scranton, served as governor of Pennsylvania in the 1960s. His older brother Teddy studied law at Cornell University but abandoned that path to manage Tim's racing career. Both brothers travelled to Europe in the early 1960s alongside future Grand Prix winner Peter Revson, and Teddy would eventually become one of the founders of the McLaren racing team alongside Bruce McLaren.
Mayer began studying English Literature at Yale in 1956 and obtained his racing licence when he turned 21 in 1959 — the minimum age permitted in America. He started that year in Sports Car Club of America events with an Austin-Healey, competing in five of thirteen national races and finishing as high as fourth at Bridgehampton. He also raced at the Nassau Speed Weeks in December, winning one race and finishing ninth in the Nassau Memorial Trophy.
For 1960 he switched to a Lotus 18 Formula Junior. After overturning the car within his first ten minutes behind the wheel, he recovered to score five second-place finishes in eight races before writing the car off when he ran into a barn at Louisville. In 1961 he acquired a Formula Junior Cooper, though military service with the US Army — beginning with basic training at Fort Dix, New Jersey and later a posting in Puerto Rico — interrupted his programme. He managed to fit in races around his leave, winning three straight rounds in a five-race series to claim the North Eastern States Formula Junior Championship.
In 1962 Mayer teamed up with Peter Revson and Bill Smith under the Rev-Em Racing banner, with Teddy managing and Tyler Alexander working on the cars. The three ran Coopers and the results were exceptional: across sixteen contests the team scored fifteen wins, fourteen second places and fourteen thirds. Mayer took victories at Marlboro, Cumberland, Bridgehampton, Elkhart Lake and Meadowdale. He finished second, behind Roger Penske's Zerex Special but ahead of Dan Gurney, in the Puerto Rico Grand Prix in November. His performances won him the SCCA Formula Junior Championship and the Kimberley Cup as the most improved and outstanding American driver of the year.
In October he stepped up to Formula One for the United States Grand Prix at Watkins Glen. The Cooper team supplied a T53 with factory support; Mayer qualified twelfth, fastest of the privateers in practice. He retired from the race on lap 31 with ignition failure and scored no World Championship points.
After completing his Army service, Mayer was given the opportunity to drive for Ken Tyrrell's team in 1963. Tyrrell ran him in Cooper T67s for a selection of European and British Formula Junior rounds, though the BMC engines were down on power compared to the Fords used by rivals such as Brabham, Lola and Lotus. He recorded finishes of third and fourth at Roskilde and Clermont-Ferrand and placings of sixth and seventh at Reims and Rouen, while in British rounds he was sixth at Brands Hatch and fourth at Snetterton. A crash at Silverstone in the British Grand Prix support race ended his day, and a brake caliper failure at Goodwood during the Tourist Trophy Junior left him with a badly twisted neck.
He also drove a factory Mini Cooper S in the last three rounds of the British Saloon Car Championship, finishing fifteenth at Brands Hatch, thirteenth at Oulton Park and eighth at Snetterton. In August he flew his own Cooper Monaco from America to contest the Guards Trophy sports car race at Brands Hatch, finishing third behind Roger Penske and Roy Salvadori.
By year's end he was signed as a works Cooper Formula One driver for 1964 alongside Bruce McLaren. Tyler Alexander later said of the signing: "Bruce had a lot of respect for Tim. That wouldn't have happened unless Bruce approved it. He realised that Tim was pretty damn quick."
The McLaren team's first entries in a championship series came in the 1964 Tasman Series, where Mayer and McLaren drove Cooper T70 cars that had been modified by the team. The series ran across New Zealand and Australia through January and February.
Mayer was immediately competitive. At Levin he finished second behind Denny Hulme. He was third in the New Zealand Grand Prix at Pukekohe before an eighth at Wigram. At Teretonga, with Hulme leading by ten seconds before damaging his suspension, McLaren won ahead of Mayer by a tenth of a second. At the Australian Grand Prix at Sandown, Mayer finished fourth in a difficult 63-lap race after struggling with a fuel-related engine miss. At Warwick Farm, where he and McLaren swapped cars, he finished third. At Lakeside he ran at the front from the start but retired on lap 15 with engine problems.
The eighth and final round was the South Pacific Trophy at Longford, held on a closed public-roads course passing over a railway crossing and lined with trees and houses. Teddy Mayer recalled: "He was getting quicker and quicker in the car with more experience and more driving time. He was faster than Bruce a lot of the time, which was pretty amazing." During Friday afternoon practice, pushing hard through a fast downhill right-hander, Mayer suddenly lost control. The car became airborne at a hump, landed badly, went out of control, and struck a tree at the edge of the circuit. The chassis broke in two at the front of the cockpit. Mayer was thrown from the wreck and died instantly.
Wreckage from the car narrowly missed young children who were spectating at the trackside. A memorial stone was placed on the roadside at the site of the accident; it was later moved and is now displayed alongside Mayer's helmet at the Country Club Hotel in Longford. He was buried in Hickory Grove Cemetery in Waverly, Lackawanna County, Pennsylvania, survived by his wife Garril, his mother Marion, and his brother Teddy.
Bruce McLaren's eulogy, written in his 1964 book From the Cockpit, became one of the most quoted passages in motorsport:
"The news that he had died instantly was a terrible shock to all of us, but who is to say that he had not seen more, done more and learned more in his 26 years than many people do in a lifetime? To do something well is so worthwhile that to die trying to do it better cannot be foolhardy. It would be a waste of life to do nothing with one's ability, for I feel that life is measured in achievement, not in years alone."
Teddy Mayer remained in motorsport after a long period of reflection following his brother's death. Alongside Tyler Alexander, he helped run the McLaren team until 1980, overseeing Formula One World Championships with Emerson Fittipaldi in 1974 and James Hunt in 1976, as well as Indianapolis 500 victories. Tyler Alexander described the driver they lost: "He was just a very personable, likeable guy. I think he was bloody good. He was getting better and better with every single race in that Tasman series."