The problem of variable susceptibility to dross formation or cast-to-cast variations in the performance of solid-state laser fusion cutting of 2 mm stainless steel sheets is investigated. The conducted study considered five different steel batches that each fully meets the material specifications of AISI 304 steel but show variations in minor element concentrations, particularly with respect to the sulfur content. Based on the hypothesis that the dross formation phenomenon correlates with surface tension and viscosity of the melt, the general melt flow behavior of the batches was first characterized by complementary experimental and simulative investigations. This combined approach allowed for a qualitative distinction of batches with a primary negative or positive temperature coefficient (NTC/PTC) of surface tension. Subsequent cutting experiments on qualitatively different batches with variations in cutting speed and gas pressure give evidence that an experienced wider processing window for dross-free cuts relates to PTC batches. However, these batches showed more irregular cut edge topography with slightly increased roughness values. It is consequently concluded that proper quality management in laser cutting of different batches of a material needs to consider the real composition of the materials being cut.