PURPOSE: To enable a workpiece to be cut in two directions orthogonal to each other by providing in a band sawing machine a saw blade guide device for twisting the edge of band saw blade to be directed in the direction of relative movement of a work table and a cutting head.

CONSTITUTION: While a workpiece W is mounted on a work table 5 and the edge of a band saw blade 25 is directed to the right hand, a cutting head 19 is moved rightward, so that the workpiece W is cut vertically. Also, while saw blade guide devices 27A, 27B are pivoted to hold the edge of band saw blade 25 directed orthogonally to this paper surface, while the work table 5 is moved so that the band saw blade 25 corresponds to the rear end of workpiece W, and then the side of workpiece W orthogonal to that which was cut previously is cut. That is, the vertical cutting of workpiece W and the cutting in the direction orthogonal to the vertical one are carried out so that the cutting and separating of test pieces or the like can be accurately carried out with a single unit of vertical band sawing machine.