A control device for a machine tool and a machine tool capable of easily performing cutting with vibration according to the amount of feed is provided. A control device (180) for a machine tool comprises a control means (181) for controlling the relative rotation and feeding of a cutting tool and a material, the control means performing control such that cutting is performed with vibrating the cutting tool relative to the material by combining a forward feed movement in the machining direction, in which the cutting tool machines the material, and a return movement in the counter-machining direction. A return position calculation section (191) for calculating a return position of the cutting tool at time when one vibration is completed on the basis of the number of vibrations and an amount of feed that are predetermined for one rotation of the cutting tool or the material, a forward feed setting section (192) for setting the forward feed movement on the basis of one or more change point setting values that determine a change point from the machining direction to the counter-machining direction, and making the cutting tool reach the determined change point, and a return movement setting means (193) for setting a pulse-like signal that is output as a command for the return movement so that the cutting tool reaches the calculated return position at time when one vibration is completed are included.