A cutting tap comprising: a plurality of thread ridges arranged at a constant pitch in an axial direction, and formed such that with an effective diameter (d 1) of the thread ridges uniform in the axial direction, a major diameter of the thread ridges gradually decreases toward an axial front side of the cutting tap; and roots formed between the respective axially adjacent pairs of thread ridges, wherein the respective thread ridges have effective diameter (d 1) reliefs by which the effective diameter (d 1) gradually decreases from a front side toward a rear side of each of the thread ridges in a rotation direction of the cutting tap, the effective diameter (d 1) reliefs being set at zero or a minute value, and wherein the respective roots have root diameter(d 2) reliefs by which a root diameter (d 2) of the roots gradually decreases from a front side toward a rear side of each of the roots in the rotation direction of the cutting tap, the root diameter (d 2) reliefs being set to be equal to the effective diameter (d 1) reliefs, characterized in that the cutting tap further comprises a plurality of deburring thread grooves formed in some or all of the roots at a constant pitch toward the axial front side of the cutting tap from rearmost ones of said some or all of the roots such that a groove bottom diameter (d 3) of the deburring thread grooves gradually decreases toward the axial front side of the cutting tap, wherein the respective deburring thread grooves have groove bottom diameter (d 3) reliefs by which the groove bottom dimeter (d 3) gradually decreases from a front side toward a rear side of each of the deburring thread grooves in the rotation direction of the cutting tap, the groove bottom diameter (d 3) reliefs being set to be larger than the effective diameter (d 1) reliefs of the thread ridges. a plurality of thread ridges arranged at a constant pitch in an axial direction, and formed such that with an effective diameter (d 1) of the thread ridges uniform in the axial direction, a major diameter of the thread ridges gradually decreases toward an axial front side of the cutting tap; and roots formed between the respective axially adjacent pairs of thread ridges, wherein the respective thread ridges have effective diameter (d 1) reliefs by which the effective diameter (d 1) gradually decreases from a front side toward a rear side of each of the thread ridges in a rotation direction of the cutting tap, the effective diameter (d 1) reliefs being set at zero or a minute value, and wherein the respective roots have root diameter(d 2) reliefs by which a root diameter (d 2) of the roots gradually decreases from a front side toward a rear side of each of the roots in the rotation direction of the cutting tap, the root diameter (d 2) reliefs being set to be equal to the effective diameter (d 1) reliefs, characterized in that the cutting tap further comprises a plurality of deburring thread grooves formed in some or all of the roots at a constant pitch toward the axial front side of the cutting tap from rearmost ones of said some or all of the roots such that a groove bottom diameter (d 3) of the deburring thread grooves gradually decreases toward the axial front side of the cutting tap, wherein the respective deburring thread grooves have groove bottom diameter (d 3) reliefs by which the groove bottom dimeter (d 3) gradually decreases from a front side toward a rear side of each of the deburring thread grooves in the rotation direction of the cutting tap, the groove bottom diameter (d 3) reliefs being set to be larger than the effective diameter (d 1) reliefs of the thread ridges.