An improved apparatus for cutting an enveloped body, which consists of an assembly having at least three circumferentially disposed cutting members, each cutting member having at least two sliding surfaces. The cutting members are assembled in sliding contact with each other such that the sliding surfaces of adjacent cutting members are slidable along each other so as to form or close a central opening surrounded by the cutting members. The opening is opened and closed for cutting the enveloped body passing therethrough. One sliding surface of a cutting member forms a convex surface, and the other sliding surface forms a concave surface complementary to the convex surface, so that the convex surface of a cutting member slides on the concave surface of an adjacent cutting member.