The machine comprises two independent units of wheels (2,4) set in succession for longitudinally moving the profiled sections (1) which are to be cut. Two or more cutting heads (6) are set for alternate action with the rear unit of the wheels (4). Each cutting head holds a circular saw blade (8) displaceable across the displacement of the profiles along the machine. Each head can be moved individually into its position where the precise position is set for that cut which has to be carried out. The saw blades are held in the cutting heads by support arms set in a rotatable fastening which defines the mobility during displacement of the saw blade along the circular path which intersects with the passing area of the profiles being cut.