His father was Mykhailo, and his sons were Stepan and Fedir. He was born in Rohoshchi. The date of his birth is unknown. Sulyma was a member of the petty gentry, and managed the estates of other nobles in the Pereiaslav region, Stanisław Żółkiewski and the Daniłowicz family, and eventually was given the villages of Sulymivka, Kuchakiv, and Lebedyn in 1620.
He then left his lands for the Zaporozhian Sich, and was elected hetman for the first time in 1628. He led many campaigns against the Turks and the Crimeans. For these efforts he received a from Pope Paul V. Because the Polish Commonwealth had been controlling and exploiting Ukraine, he decided on his way back from campaign in Crimea to rebel against Poland. In 1635 he attacked and destroyed the Polish castle at Kodak, which was constructed on the Dnieper River to contain the Kozaks. He killed all the German mercenaries and the fortresses commander. After his armies were defeated, the other kozaks turned him and his fellow rebels over to the Poles. He was executed in Warsaw on December 12, 1635. Sulyma was tortured and cut to pieces, as a warning that revolts would not be tolerated.