A cutting insert comprising: a substrate; and a cutting-edge insert; wherein the substrate has in a thickness direction of the substrate a bottom surface, and a top surface opposite to the bottom surface, the top surface has a polygonal shape composed of a plurality of sides in a plan view as seen along the thickness direction, the top surface is provided with a projection projecting to a side opposite to the bottom surface along the thickness direction, the projection has a through-hole passing through the substrate along the thickness direction, the projection has a side surface contiguous to the top surface, the side surface is composed of a curved line protruding to a side opposite to the through-hole in the plan view as seen along the thickness direction, the curved line includes a plurality of vertices (P1, P2, P3, P4) at positions at which the curved line has a minimum distance from the plurality of sides, respectively, the cutting-edge insert is brazed to the top surface and the side surface so as to annularly surround the projection, and is characterised in that, the cutting-edge insert includes a plurality of divided pieces, a number of the plurality of divided pieces is equal to a number of the plurality of sides, the plurality of divided pieces in a longitudinal direction extend along the plurality of sides, respectively, each of the plurality of divided pieces has in the longitudinal direction a first end, and a second end opposite to the first end, each of the plurality of divided pieces has a first protrusion at the first end, and a second protrusion at the second end, the first protrusion of one divided piece among the plurality of divided pieces retains the second protrusion of another divided piece among the plurality of divided pieces between the side surface and the first protrusion of the one divided piece, the other divided piece being adjacent to the one divided piece, and positions of centers of gravity (P5, P6, P7, P8) of the plurality of divided pieces are displaced from the plurality of vertices, respectively, in the longitudinal direction. a substrate; and a cutting-edge insert; wherein the substrate has in a thickness direction of the substrate a bottom surface, and a top surface opposite to the bottom surface, a bottom surface, and a top surface opposite to the bottom surface, the top surface has a polygonal shape composed of a plurality of sides in a plan view as seen along the thickness direction, the top surface is provided with a projection projecting to a side opposite to the bottom surface along the thickness direction, the projection has a through-hole passing through the substrate along the thickness direction, the projection has a side surface contiguous to the top surface, the side surface is composed of a curved line protruding to a side opposite to the through-hole in the plan view as seen along the thickness direction, the curved line includes a plurality of vertices (P1, P2, P3, P4) at positions at which the curved line has a minimum distance from the plurality of sides, respectively, the cutting-edge insert is brazed to the top surface and the side surface so as to annularly surround the projection, and is characterised in that, the cutting-edge insert includes a plurality of divided pieces, a number of the plurality of divided pieces is equal to a number of the plurality of sides, the plurality of divided pieces in a longitudinal direction extend along the plurality of sides, respectively, each of the plurality of divided pieces has in the longitudinal direction a first end, and a second end opposite to the first end, a first end, and a second end opposite to the first end, each of the plurality of divided pieces has a first protrusion at the first end, and a second protrusion at the second end, a first protrusion at the first end, and a second protrusion at the second end, the first protrusion of one divided piece among the plurality of divided pieces retains the second protrusion of another divided piece among the plurality of divided pieces between the side surface and the first protrusion of the one divided piece, the other divided piece being adjacent to the one divided piece, and positions of centers of gravity (P5, P6, P7, P8) of the plurality of divided pieces are displaced from the plurality of vertices, respectively, in the longitudinal direction.