Cutting tip for rotating cutting tool and rotating cutting tool using the tip, and method of machining using the tool

The present invention provides a cutting insert, a rotating cutting tool holding said cutting insert and a cutting method using the tool which is able to prevent the occurrence of burrs and to cut a smooth finished surface. In a rotating cutting tool which carries a plurality of cutting inserts, at least one insert is made of single crystal diamond 3 A, and the minor cutting edge of the insert has an arc shaped portion whose radius is in the range of 10 mm or more to 500 mm or less. A high hard material other than single crystal diamond, for example PCD 3 B, is used for the remainder of the cutting inserts. It is preferable that a cutting edge of single crystal diamond 3 A be projected to the rotating axis direction in the range of 0.01 mm or more to 0.05 mm or less, compared with the cutting edges of high hard material.