The paper shows the influence of plasma cutting modes on the surface structure and properties of pure copper sheets having different thickness. It is found that plasma cutting is complicated by dynamic processes of melting, flow and crystallization of metal displaced from the cutting cavity by the plasma jet. Intensive heat dissipation and inhomogeneous metal flow lead to the debris formation at the cut bottom, which grows with increasing thickness of copper sheets. After plasma cutting, the macrostructure in the work area of sheets comprises melting zone, heat-affected zone, and unaffected base metal. Intense localized metal boiling on the cut surface leads to the formation of a highly porous structure. The cut morphology, including the melting zone and heat accumulation, depends on the cutting modes.