Cutting device, method and use are for cutting of a line extending from a floating vessel. The cutting device is structured for placement on the vessel. The cutting device comprises: at least one guide structured for directional steering of the line past a cutting area for the line; and at least one of the following cutting-promoting devices: at least one induction coil device directed inwards toward the cutting area and structured for heating, hence weakening, of the line within the cutting area; and at least one moveable cutting knife with an opposite contact surface directed inwards toward the cutting area and also structured for cutting of the line within the cutting area.