An ethnic Pole from Ukraine, Śliwiński represented the USSR at the 1988 Olympics, winning the Canadian canoe C-1 500 m silver medal at the age of only eighteen.

The break-up of the Soviet Union affected Śliwiński's career greatly as the newly independent Ukraine did not win any world championship gold medals during the 1990s.

Śliwiński, now specialising in the short sprint 200 m races, was still regarded as a top competitor at international events but he endured a frustrating sequence of four world championship bronze medals.

However, when a member of Poland's four-man (C-4) 1000 m crew, Arkadiusz Tonski, also had to pull out injured, Śliwiński was called up as a last-minute replacement.

The Polish four, ironically including the now rehabitated Gajownik, edged out the Romanian crew to take the gold medal.