Stamsnijder was military cyclo-cross world champion in 1975. In 1976 he took part in the Olympic Games.[1] In 1979 he won the Essen cyclo-cross and the amateur Dutch road race championship. In 1980 he turned professional for DAF Trucks, finishing third in the cyclo-cross world championship.
Stamsnijder's greatest success was becoming cyclo-cross world champion in 1981 in Tolosa in the Basque Country. On a muddy course he left the Belgian Roland Liboton and the Swiss champion Albert Zweifel behind him to take the title. Stamsnijder was the first Dutch world cyclo-cross champion and that year he was named sportsman of the year.
Stamsnijder rode the Tour de France in 1980 and 1981, but it was cyclo-cross that brought his greatest victories, winning the Superprestige classification in 1983, 1984, 1987 and 1989 with 14 wins in Superprestige races.[2]
In 1989 Stamsnijder ended his career when his son fell ill. He became the coach of the Dutch cyclo-cross team and is now a manager of Shimano sports marketing. His son, Tom Stamsnijder, was a professional cyclist too.