A cutting device and method are provided for cutting a tire component. The cutting device comprises a support surface for supporting the tire component, a cutter which is movable along a cutting line for cutting through the tire component on the support surface, and a pressing device which is movable along the cutting line for pressing the tire component onto the support surface. The cutting device is arranged to move the pressing device from a first position at the support plane to a second position at a clearance height from said support plane in a clearance direction transverse or perpendicular to the support plane, and from the second position towards the first position in a pressing direction opposite to the clearance direction.

A cutting device and a method for cutting a tire component are provided. The cutting device comprises a conveyor that defines a conveyor plane. The cutting device comprises a lifting beam for lifting the tire component up from the conveyor plane in a lift direction. The cutting device is provided with a knife for cutting the tire component along a cutting line intersecting with the lifting beam at a cutting center at an oblique cutting angle. The cutting device is provided with a first hold-down unit for holding down the tire component towards the conveyor in a hold-down direction opposite to the lift direction. The first hold-down unit comprises a contact member for holding down the tire component in the hold-down direction towards the conveyor at a first hold-down position within a hold-down radius of less than one-hundred-and-fifty millimeters from the cutting center.