Taylor was born in Pencaitland, East Lothian, and entered his first sidecar race in 1974 as passenger to Kenny Andrews. The following year he began racing as a driver in his own right. He won the Scottish Sidecar Championship with passenger Lewis Ward in 1977, competing at circuits including East Fortune near Haddington, Beveridge Park in Kirkcaldy, and Knockhill near Dunfermline.
In 1978 Taylor decided to step up to Grand Prix racing and the British Championships. He parted with Ward and teamed up with a new passenger from nearby Haddington, Jimmy Neil. The new partnership took time to find its rhythm, but by the end of the season the pair were winning regularly in England.
In 1979 Taylor acquired a Seymaz hub steering outfit, but suffered two accidents in it, one of which resulted in the death of stand-in passenger Dave Powell at Oulton Park. With Neil injured, Taylor used veteran passenger Jimmy Law for the German GP at Hockenheim on his old Windle-framed Yamaha, finishing fifth. It was when Taylor paired with Swedish former 125cc rider Benga Johansson that the breakthrough finally came: the duo claimed Taylor's first Grand Prix victory at the Swedish TT at Karlskoga later that year.
In 1980 Taylor and Johansson won four Grand Prix races and finished on the podium at every event they completed. Taylor won the British Championship and triumphed at the Isle of Man, winning the Sidecar TT overall. In 1981 he retained his British title and extended his TT record to four wins.
In 1982, Taylor and Johansson raised the sidecar lap record at the Isle of Man TT to 108.29 mph (174.27 km/h), a benchmark that stood for seven years and demonstrated the exceptional pace the partnership had developed on the demanding Mountain Course.
The 1982 Finnish Grand Prix was held at Imatra in very wet conditions. During the race, Taylor and Johansson's machine began to aquaplane and slid off the road, colliding with a telephone pole. While emergency services worked to remove Taylor from the wreckage, a second sidecar slid off the circuit and struck the rescue crew. Taylor died in hospital later that evening. He was 28 years old.
Taylor was buried in the local cemetery at Pencaitland. A memorial was erected in the village in December 2006. A second memorial stands in Beveridge Park in Kirkcaldy, overlooking Railway Bend on the old motorcycle racing circuit. A further memorial to Taylor is located in Imatra, near the paddock of the Finnish championship racetrack.
Taylor's world championship-winning and TT lap record-winning sidecar was purchased by friend and fellow competitor Jack Muldoon from Taylor's sponsor Dennis Trollope. The machine spent time in a museum in Alford, Aberdeenshire, but was never properly restored there. Muldoon and his family acquired the sidecar in March 2012 and carried out a complete restoration, stripping the chassis to bare metal, replacing all bearings, and fully rebuilding the Yamaha TZ700 engine — the first time it had run in 30 years. The restored machine was paraded at the Jock Taylor Memorial race weekend at East Fortune in August 2012.
From the year following his death, an annual end-of-season race at Knockhill was established in Taylor's honour: the Jock Taylor Trophy. The event has drawn the leading sidecar crews from across the United Kingdom each year, becoming one of the most prestigious non-championship events on the British sidecar calendar.