Control device for machine tool and machine tool

A control device for a machine tool and a machine tool, for which settings of the number of vibrations per rotation become easy, is provided. The control device of the machine tool controls a relative rotation between a workpiece and a cutting tool and a relative reciprocal movement between the workpiece and the cutting tool in a feed direction to perform vibration cutting to the workpiece. The control device includes a control section for controlling a spindle headstock, a first tool post, and a second tool post, the workpiece W being installed on the spindle headstock, the first tool post being provided to be reciprocally movable along the feed direction with respect to the spindle headstock and installed with a first cutting tool for cutting the workpiece, and the second tool post being provided to be reciprocally movable along the feed direction with respect to the spindle headstock independently of the first tool post and installed with a second cutting tool for cutting the workpiece.