An internal milling cutter comprising a ring shaped carrier disk having an outer circumference, an inner circumference, a centre axis defining an axis of rotation of the milling cutter, and a plurality of separated tool holder segments removably mounted at the inner circumference of the carrier disk, and at least one clamp for each tool holder segment mounted on the carrier disk, wherein the plurality of tool holder segments together form a ring, wherein each of the tool holder segments at its inner circumference comprises at least one cutting insert seat with a mounting element for a cutting insert (6, 7) Z and a cutting insert mounted in the insert seat or at least one cutting edge, wherein the carrier disk comprises an axial abutment surface for each of the tool holder segments providing a support of the tool holder segment in an axial direction of the carrier disk, wherein each of the tool holder segments comprises an axial contact surface in engagement with the axial abutment surface of the carrier disk, and wherein the respective clamp is located and arranged such that it generates a force in the axial direction pressing the axial contact surface of the respective tool holder segment onto the axial abutment surface of the carrier disk, wherein the clamp is mounted movably in a radial direction of the carrier disk between a locking position and a releasing position, wherein in the locking position the clamp is in engagement with the carrier disk and the tool holder segment preventing an axial separation of the carrier disk and the tool holder segment, and wherein in the releasing position the clamp allows a separation of the carrier disk and the tool holder segment in the axial direction of the carrier disk, characterised in that, the clamp is slidably mounted, wherein the clamp is formed by a shim and wherein in a surface of the tool holder segment a pocket is formed, wherein the shim in the locking position engages with the pocket, the shim having a protrusion protruding in an axial direction of the carrier disk towards the tool holder segment, wherein the protrusion in the locking position of the shim is in engagement with a recess formed in the pocket of the tool holder segment. a ring shaped carrier disk having an outer circumference, an inner circumference, a centre axis defining an axis of rotation of the milling cutter, and a plurality of separated tool holder segments removably mounted at the inner circumference of the carrier disk, and at least one clamp for each tool holder segment mounted on the carrier disk, wherein the plurality of tool holder segments together form a ring, wherein each of the tool holder segments at its inner circumference comprises at least one cutting insert seat with a mounting element for a cutting insert (6, 7) Z and a cutting insert mounted in the insert seat or at least one cutting edge, wherein the carrier disk comprises an axial abutment surface for each of the tool holder segments providing a support of the tool holder segment in an axial direction of the carrier disk, wherein each of the tool holder segments comprises an axial contact surface in engagement with the axial abutment surface of the carrier disk, and wherein the respective clamp is located and arranged such that it generates a force in the axial direction pressing the axial contact surface of the respective tool holder segment onto the axial abutment surface of the carrier disk, wherein the clamp is mounted movably in a radial direction of the carrier disk between a locking position and a releasing position, wherein in the locking position the clamp is in engagement with the carrier disk and the tool holder segment preventing an axial separation of the carrier disk and the tool holder segment, and wherein in the releasing position the clamp allows a separation of the carrier disk and the tool holder segment in the axial direction of the carrier disk, characterised in that, the clamp is slidably mounted, wherein the clamp is formed by a shim and wherein in a surface of the tool holder segment a pocket is formed, wherein the shim in the locking position engages with the pocket, the shim having a protrusion protruding in an axial direction of the carrier disk towards the tool holder segment, wherein the protrusion in the locking position of the shim is in engagement with a recess formed in the pocket of the tool holder segment.