Method and apparatus for severing tire ply stock (S) wherein the apparatus includes a knife assembly (14) utilizing a blade (50) having a curved leading edge (58) and a straight trailing edge (62) which meet at a leading point (66). The ply stock (S) is supported by a slotted anvil (26) in the area immediately adjacent a cut line. In operation, the knife assembly (14) is lowered and the leading point (66) pierces the ply stock (S) between adjacent cords. During the downward stroke, the trailing edge (62) back-cuts the ply stock (S) from the insertion point (98) to a first lateral edge (18). The leading edge (58) severs the remainder of the ply stocks (S) as the knife assembly (14) traverses the ply stock to a second lateral edge (22).