To solve the problem of a conventional steel pipe cutting apparatus causing vibrations and resulting noises and chipping of a band saw when cutting the portion of a steel pipe near its diameter, because of a structure for slicing the steel pipe while fixing.

The apparatus for cutting a steel pipe while rotating it comprises a cutter; an end support device for supporting the rear end of the steel pipe; a feeder supporting the end support device in such a manner that the support device is movable along the axis of the steel pipe; and a rotating support device for supporting the portion of the steel pipe near its cut section. A method of cutting the steel pipe while rotating it includes making a cut in the overall area of the outer peripheral surface of the steel pipe with the cutter; then stopping the rotation of the steel pipe; making a cut up to the inner peripheral surface of the steel pipe; and then rotating the steel pipe again.