The sawing machine comprises a guide pulley composed of a plurality of wheels of the same diameter, coaxial and mutually juxtaposed side by side in a pack on a corresponding shaft or the likeAccording to the invention, in said wheel pack of the guide pulley (P2) a wheel (P21) presenting at least an external circumferential groove (P21′) and a wheel (P22) presenting a plurality of external circumferential grooves (P22′) are alternated in a repetitive sequence. Said wheels (P21, P22) comprise a radially internal part (P21.1, P22.1), at which they are mutually juxtaposed in a pack. Each wheel (P21) presenting at least a groove (P21′) comprises a radially external part (P21.2) having an external annular rim (P21.3) of lesser width than the thickness of said internal part (P21.1) thereof, while each wheel (P22) presenting a plurality of grooves (P22′) comprises a radially external part (P22.2) having an external annular rim (P22.3) of a width greater than the thickness of said internal part (P22.1) thereof, and which overlaps, laterally, partially and in a freely revolving manner, the radially internal part (P21.1) of each wheel (P21) adjacent and presenting at least a groove (P21′)