Seaman was born in Aldingbourne House near Chichester, Sussex, into a wealthy family. He grew up initially at Kentwell Hall, Long Melford, Suffolk, developing an early enthusiasm for motoring. After Rugby School he went up to Trinity College, Cambridge, where his first competitive experience came at the 1931 Shelsley Walsh Speed Hill Climb. His parents hoped he might enter Parliament or the law.
Seaman made rapid progress through domestic and continental events in the mid-1930s. He won the voiturette race of the Swiss Grand Prix at Bremgarten on his first attempt and went on to take that event three times consecutively. Competing with English Racing Automobiles machinery at Brooklands and Donington Park, he claimed further victories in the junior categories of leading events.
In 1935 Seaman had a productive ERA season, taking pole at the Dieppe Grand Prix and winning the junior class at the Coppa Acerbo, as well as the Czech Masaryk Grand Prix in September. His 1936 campaign is considered the peak of his early career: with a highly developed 1926 1,500 cc Delage that had been modified to become highly competitive, he won the British Empire Trophy at Donington Park and the 1936 Donington Grand Prix, the latter shared with Hans Ruesch. He also won his class at the Freiburg hillclimb, finishing barely a second behind overall winner Hans Stuck. These results drew the attention of Mercedes team chief Alfred Neubauer, who invited Seaman for a trial at the Nurburgring.
Seaman signed for Mercedes for 1937 despite his mother's strong objections to his driving for a team associated with the Nazi government. His opening season was disrupted when he was involved in the fatal accident of Ernst von Delius at the German Grand Prix, injuries preventing him from racing at Monaco and at Pescara. He recovered to finish fourth at the Italian Grand Prix at Livorno and repeated that result at the non-championship Czech Grand Prix at Brno. Neubauer relegated him to reserve status at the Swiss Grand Prix. Outside Europe, Seaman finished second to Bernd Rosemeyer at the AAA-sanctioned Vanderbilt Cup in Long Island.
The 1938 season brought Seaman's greatest triumph. At the German Grand Prix — the most prestigious race of the year for the German Silver Arrows teams — he drove to victory, becoming a favourite of Adolf Hitler and prompting Mercedes dealerships worldwide to display his photograph. After a postseason break, Seaman returned to take pole and finish second at the Swiss Grand Prix at Bremgarten, a circuit he particularly favoured, and finished third at his home event at Donington Park. His biographer George Monkhouse judged the wet-conditions drive at Bremgarten the finest of Seaman's career.
Seaman had a slow start to 1939. He attended the French Grand Prix without competing, and Neubauer barred him from the Tripoli Grand Prix. At the Eifelrennen at the Nurburgring he retired early with a broken clutch.
Leading the Belgian Grand Prix at Spa-Francorchamps during a wet race, Seaman crashed his car into a tree on lap 22, believed to have been using a dry-weather line through a corner inappropriate for the conditions. The car caught fire with the unconscious driver inside. He died of his burns a few hours later. On his deathbed he told Mercedes' chief engineer: "I was going too fast for the conditions — it was entirely my own fault. I am sorry." The accident was Mercedes' only driver fatality during the pre-war Silver Arrows era.
Seaman divided his time between the family home at Pull Court in Worcestershire and London. In December 1938 he married Erica Popp, the 18-year-old daughter of the director of BMW, with her father purchasing the couple a Bavarian home as a wedding gift. Following Seaman's death, Erica spent the war years in Britain and the United States and married twice more, dying in Sarasota, Florida, in February 1990. Richard Seaman was buried at Putney Vale Cemetery in London.
Seaman is widely regarded, alongside Henry Segrave, as one of Britain's greatest pre-war Grand Prix drivers. His legacy carries the complication of his Mercedes association: biographers note that Seaman simply sought the fastest available machinery regardless of politics, yet he was privately complimentary of Hitler and controversially gave a version of the Nazi salute — described as "distinctly unemphatic" — after his 1938 German Grand Prix victory. The largest wreath at his funeral was sent by Hitler, against the wishes of his family. A memorial stone was installed at Spa-Francorchamps but later went missing and was never recovered.