The machine has a sawing unit (3) movable along a straight cut line (2) for cutting a workpiece (1) lying on or at a surface (4) of a machine table (5). A support unit (6) is arranged on the machine table, where a support surface (7) of the support unit supports the workpiece. The support surface is moved from a retracted position into an advanced position by a support drive (8). The surface lies on a side (9) below the table surface during operation of the machine in the retracted position, and lies on another side (10) above the table surface during operation in the advanced position.
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