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 3A, 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 3B, is used for the remainder of the cutting inserts. It is preferable that a cutting edge of single crystal diamond 3A 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.