Blignaut raced locally within South Africa for many years, establishing himself as a competitive presence in the country's club and national racing scene before attempting to step up to international level. His most prominent appearances as a driver came in the non-championship Formula One Rand Grand Prix, a prestigious event held annually at Kyalami and other South African circuits. He entered in 1963 and again in 1964 under the Team Valencia banner, finishing 12th on both occasions.
His one attempt to enter a World Championship Formula One race came at the 1965 South African Grand Prix, which was held at East London. Blignaut entered the event but withdrew before it took place, meaning he never scored a World Championship result as a driver.
After stepping away from the cockpit, Blignaut redirected his energy into team management, founding the Alex Blignaut Racing Team. The team entered cars in the South African Formula One Championship throughout the late 1960s and early 1970s, accumulating many race victories in a domestic series that attracted a strong field of local talent and occasionally drew in drivers with international ambitions.
Among the most notable drivers to race for Blignaut were Eddie Keizan and Ian Scheckter — two figures who represented the strength of South African open-wheel racing during that period. Keizan in particular forged a strong association with the team, and Blignaut gave him the opportunity to compete at the highest level by entering him in a Tyrrell 004 at the South African Grand Prix in both 1973 and 1974. These were championship rounds of the Formula One World Championship, giving Blignaut's team its highest-profile international exposure.
Beyond his roles as driver and team owner, Blignaut served as secretary of SAMRaC — the South African Motor Racing Club — the body responsible for organising the South African Grand Prix at Kyalami. His tenure in this administrative position placed him at the centre of the country's motorsport governance during a period when the South African Grand Prix was a regular and respected fixture on the Formula One World Championship calendar, and Kyalami was regarded as one of the more technically demanding and atmospheric circuits in the sport.
Blignaut embodied the profile of the committed regional motorsport figure: a driver turned owner turned administrator whose decades of involvement helped sustain South African motor racing as a viable ecosystem capable of producing world-class talent. The careers of drivers like Keizan benefited directly from the infrastructure and opportunity that operators like Blignaut provided at club and national level.
He died on 15 January 2001 following an accident on his farm, where he was electrocuted while repairing a piece of machinery.