An automatic sawing machine for sawing natural stones pieces and concrete blocks, said machine comprising: i) a frame; ii) a first conveyor belt and a second conveyor belt, said first conveyor belt and said second conveyor belt being both motorized and mutually arranged at right angles, the first conveyor belt and the second conveyor belt defining in a longitudinal direction a channel-like cutting path suitable to receive consecutive natural stones pieces or concrete blocks to be cut; iii) a plurality of cutting devices, each cutting device comprising a motor on whose shaft a circular blade is keyed, said cutting devices being restrained to said frame subsequent to each other in said longitudinal direction and being arranged above the channel-like cutting path defined by the conveyor belts (120, 130) with respect to a vertical direction, perpendicular to the longitudinal direction, so that the respective circular blades are located within the channel-like cutting the path; iv) a positioning device configured to maintain said blocks in contact with the conveyor belts (120, 130) that define the cutting path during their processing, wherein that said positioning device comprises a bar restrained to the frame in the longitudinal direction of the automatic sawing machine parallel to the cutting path defined by the conveyor belts (120, 130), said bar comprising a plurality of arms pivotally restrained thereto and urged away therefrom by way of a respective tensioning device, wherein the bar of the positioning device is mounted movably perpendicularly to the cutting path defined by the conveyor belts (120, 130), and in that the conveyor belts (120, 130) are mounted movably relative to the frame and wherein said automatic sawing machine further comprises a plurality of guiding members arranged between pairs of circular blades that are consecutive to each other in the longitudinal direction, wherein each guiding member comprises a support fixed to the frame of the automatic sawing machine in the zone comprised between two consecutive cutting devices and a sheet metal plate lying on the same plane of the circular blades, said sheet metal plate extending in the vertical direction and progressively widening in the longitudinal direction from said support, the overall configuration of the guiding member being such that the sheet metal plate forms together with the circular blades a surface that is substantially continuous in the longitudinal direction.. i) a frame; ii) a first conveyor belt and a second conveyor belt, said first conveyor belt and said second conveyor belt being both motorized and mutually arranged at right angles, the first conveyor belt and the second conveyor belt defining in a longitudinal direction a channel-like cutting path suitable to receive consecutive natural stones pieces or concrete blocks to be cut; iii) a plurality of cutting devices, each cutting device comprising a motor on whose shaft a circular blade is keyed, said cutting devices being restrained to said frame subsequent to each other in said longitudinal direction and being arranged above the channel-like cutting path defined by the conveyor belts (120, 130) with respect to a vertical direction, perpendicular to the longitudinal direction, so that the respective circular blades are located within the channel-like cutting the path; iv) a positioning device configured to maintain said blocks in contact with the conveyor belts (120, 130) that define the cutting path during their processing,