At his first Olympic appearance in 1956, Wolde competed in the 800 m, 1,500 m and the 4x400 relay. He didn't compete in the 1960 Summer Olympics, when Abebe Bikila became the first Ethiopian to win a gold medal. Wolde claimed his absence was due to the government's desire to send him on a peacekeeping mission to the Congo during the Congo Crisis. According to him, in the government's ensuing conflict with the Ethiopian Olympic Committee, who wanted him to compete, he didn't get sent to either event. However, athlete Said Moussa Osman, who represented Ethiopia in the 800 m at the 1960 Olympics, stated that Wolde lost at the trials and didn't make it on the team.
Beginning in the 1960s, Wolde's focus changed from middle distance races to long distances. He placed fourth in the 10,000 m at the 1964 Summer Olympics, which was won by Billy Mills of the United States in one of the biggest upsets in the history of Olympic competition. After Abebe Bikila had won the 1964 Olympic marathon, four years later at the 1968 Summer Olympics, Wolde became the second Ethiopian to win the title in the marathon. Earlier in the same Olympics, Wolde had already won the silver medal in the 10,000 m. In 1972, Wolde won a third Olympic medal at the age of 40, winning bronze in the marathon. He blamed his third place showing on ill-fitting shoes forced on him by Ethiopian officials. Nonetheless, he became only the second person in Olympic history (Bikila was the first) to medal in successive Olympic marathons. Both medalists ahead of him in 1972, Frank Shorter and Karel Lismont would repeat the feat in 1976 behind Waldemar Cierpinski who would do it in 1980. Erick Wainaina was the most recent and only other to do it in 2000. He won the marathon race of 1973 All-Africa Games.
In 1993, Wolde was arrested on the accusation that he participated in a Red Terror execution during the regime of the dictator Mengistu Haile Mariam. He argued that although he was present at the killing, he was not a direct participant. The IOC pressured the Ethiopian government to release him. In early 2002 he was convicted to six years of imprisonment, but released because he had spent nine years in detention already waiting for his trial.
Wolde died of liver cancer at age 69 a few months after his release. He had been married twice and had three children; a son with his first wife, Samuel, and two children, Addis Alem and Tabor, with his second wife. Mamo Wolde is interred in Saint Joseph's Church Cemetery in Addis Ababa, beside his fellow countryman Abebe Bikila.