To explore the role of dislocation slip mode playing in the size effect of mechanical behavior of metallic materials, the tensile behavior of Cu-5at.%Mn and Cu-20at.%Mn alloys with thickness (t) spanning from 0.1 to 2.0 mm is investigated. The results reveal that the yield strength σYS of Cu-5at.%Mn alloy displays an independence of thickness, whereas the ultimate tensile strength σUTS and the uniform elongation δ show an obvious size effect. The σUTS and δ first slightly decrease as t is reduced from 2.0 to 0.5 mm, but evidently drop when t is below 0.5 mm. A similar size effect is also exhibited in Cu-20at.%Mn alloy; however, the variation trend of “the smaller the weaker” in size effect can be weakened by the planar slip of dislocations occurring during the deformation of this alloy.