A cutting apparatus includes a blade changing apparatus for changing a cutting blade mounted on a spindle of a first cutting unit and changing a cutting blade mounted on a spindle of a second cutting unit. The blade changing apparatus includes a nut mounting and demounting unit for mounting and demounting a nut in each of the first and second cutting units and a blade mounting and demounting unit for mounting and demounting the cutting blade in each of the first and second cutting units. The nut mounting and demounting unit includes a rotating shaft, a first nut rotating portion fixed to one end of the rotating shaft, a second nut rotating portion fixed to the other end of the rotating shaft, a motor, and a power transmitting unit connected to the motor and the rotating shaft.