Degner's father died near the end of World War II, after which the family fled their Silesian hometown to escape the advancing Red Army, eventually settling in Luckau in the newly formed German Democratic Republic. His mother died shortly afterward, leaving Degner to complete his education at Potsdam Technical High School, where he earned a diploma in development engineering in 1950.
He became an apprentice motorcycle mechanic in Potsdam and joined the Potsdam Motorcycle Club, where he encountered Daniel Zimmermann, a designer who had built a fast 125cc racer called the ZPH. Degner began racing in 1952 and by 1953 had taken his first victories at Leipziger Stadtpark and Bernau, finishing runner-up in the 125cc Ausweisklasse Junior Championship. He followed that with a second-place finish in the 1955 East German 125cc Championship.
His performances attracted the attention of Walter Kaaden, team manager at the MZ factory in Zschopau, who signed Degner as an engineer-rider starting 1 March 1956. MZ competed with highly developed two-stroke engines, and Kaaden had built on principles developed by Erich Wolff at DKW concerning expansion chambers and exhaust sound waves for optimised engine tuning. Degner thrived under these conditions: in 1957 alone he won 11 of 14 125cc races and was crowned East German 125cc national champion.
From 1958, MZ entered Degner in all World Championship rounds. He scored his first Grand Prix victory at the 1959 125cc Nations Grand Prix at Monza and ended that season fifth in the 125cc world championship. A practice crash at the 1960 Isle of Man TT compromised his title challenge, but a second GP win at the Belgian Grand Prix secured him third in the 125cc standings.
The Degner family's regular travel to races in the West exposed them to stark contrasts in living standards, reinforcing their unwillingness to raise children under the GDR's authoritarian surveillance state. Planning began at the end of 1960. Knowing his expertise lay exclusively in two-stroke engines, Degner identified Suzuki and Yamaha as the manufacturers most likely to offer a competitive factory contract. He was first approached by Suzuki team manager "Jimmy" Matsumiya at the 1961 Isle of Man TT and secretly signed a consulting contract with Suzuki at the Dutch TT in Assen on 30 June 1961.
The family's original escape plan — crossing from East Berlin into West Berlin — was rendered impossible when the Berlin Wall was erected in August 1961. Degner instead arranged for his family to be smuggled out of the GDR in the trunk of a car on the weekend of 16–17 September 1961, while he was competing in the Swedish Grand Prix at Kristianstad. He needed only to finish the Swedish race well to clinch the 125cc World Championship for himself and for MZ, but his engine failed early. His chief rival, Honda's Tom Phillis, was unable to clinch the title at that race either, leaving the championship unresolved. After the race Degner drove to Gedser, Denmark, caught the ferry to Holstein-Grossenbrode in West Germany, and reunited with his family, who had already crossed safely.
MZ and the East German motorsport federation accused Degner of deliberately sabotaging his engine and had his East German racing licence revoked. An attempt to enter him in the final championship round in Argentina on an EMC 125cc motorcycle was thwarted when the machine was deliberately delayed in transit. Tom Phillis won the Argentine race and with it the 1961 125cc World Championship. An FIM court in Geneva, convened in November 1961, dismissed the charge that Degner had intentionally destroyed his MZ engine.
Suzuki fulfilled the consulting contract in November 1961, relocating Degner to Hamamatsu to spend the winter in the race shop. Using his deep knowledge of two-stroke loop-scavenge tuning perfected during his years at MZ, Degner substantially improved Suzuki's new 50cc and 125cc racing engines. The results were rapid: by 14 October 1962, Degner had won Suzuki's first-ever Grand Prix World Championship in the 50cc class.
On 3 November 1962, at the inaugural race meeting at Suzuka Circuit, a gust of wind lifted the front wheel of Degner's 50cc Suzuki as he rounded Turn 8, causing a crash. In recognition of this moment in Suzuka's history, Turn 8 was subsequently named the Degner Curve, a name it retains to this day.
The following year brought a far more serious accident. At the Japanese Grand Prix on 10 November 1963, Degner crashed his 250cc Suzuki at the exit of Turn 2 on the opening lap. The full fuel tank burst into flames. He was dragged unconscious from the fire by marshals and required more than fifty skin grafts. He was unable to return to racing until September 1964, when he won the 125cc Japanese Grand Prix. He added three more Grand Prix victories in 1965 before retiring from motorcycle racing at the end of the 1966 season.
After retirement, Degner made a brief foray into single-seater car racing and then worked as technical manager at Suzuki's German importer in Munich. He subsequently moved to Tenerife, where he operated a car hire business. He died on 10 September 1983 in Arona. His death was attributed in part to dependency on medications following the 1963 burn injuries, and rumours persisted that he had either taken his own life or been killed by the East German Stasi in retaliation for his defection. No definitive evidence supported either claim.
Degner's defection is among the most consequential acts in the history of Grand Prix motorcycle racing. The two-stroke engineering knowledge he carried from MZ to Suzuki gave the Japanese manufacturer a competitive foundation it could not have built as quickly through conventional development. MZ, deprived of both Degner and its accumulated engine knowledge, never won a Grand Prix World Championship. Suzuki, enriched by that transfer, became a multi-time world champion manufacturer in the decades that followed. The Degner Curve at Suzuka Circuit serves as a permanent physical reminder of his place in the sport's history.