To provide a cutting and burnishing apparatus and a cutting and burnishing method capable of continuously and accurately performing cutting and burnishing work even on an outer peripheral surface of a curved workpiece.

The cutting and burnishing apparatus 1 includes a cutting unit 4, a burnishing unit 5 and a conveyance unit 3. The cutting unit 4 cuts the outer peripheral surface of the workpiece W while centering the workpiece W by cutting tools 31a, 31b and 31c. In the burnishing unit 5, a burnishing roller 41 applies force of feeding the workpiece W in the conveyance direction while pressing and burnishing the outer peripheral surface of the workpiece W. The conveyance unit 3 feeds the workpiece W while holding it until the workpiece W reaches the burnishing unit 5.