A machine for cutting fruit or vegetables into segments, including a blade group (10), at least one of which is arranged with a radial orientation relative to a central axis (X); a presser (20) arranged above the blade group (10) and mobile according to an operating stroke along which it pushes a product (P) through the blades (10); a motor, connected to the presser (20) for activating it along an operating stroke thereof. The presser (20) includes a central body (21), connected to the motor; a peripheral body (22), arranged concentrically to the central body (21) and mobile relative to the central body (21) between a first and a second end position.