Cutting insert and processing method

A cutting insert having a surface involved in cutting, the surface being composed of at least one of a cBN-based sintered material, a diamond-based sintered material, a ceramic, a cermet, or a cemented carbide,

• the cutting insert comprising:
• a rake face;
• a flank face;
• and a cutting edge constituted of a ridgeline between the rake face and the flank face, wherein
• the cutting edge has
• a first cutting edge portion for corner processing,
• a second cutting edge portion for pulling processing, and
• a third cutting edge portion for finished-surface processing,
• a first connection cutting edge portion that connects the first cutting edge portion and the third cutting edge portion, and
• a second connection cutting edge portion that connects the second cutting edge portion and the third cutting edge portion,
• the third cutting edge portion is disposed between the first cutting edge portion and the second cutting edge portion,
• the first cutting edge portion has a curved shape,
• a curvature radius of the first cutting edge portion is 0.1 mm or more and 2.4 mm or less,
• the second cutting edge portion has a straight line shape or a curved shape having a curvature radius of 3 mm or more,
• the third cutting edge portion has a straight line shape or a curved shape having a curvature radius of 3 mm or more, and
• each of the first connection cutting edge portion and the second connection cutting edge portion has a curved shape.