The invention relates to a sawing system (Sg) for mounting in a machine for cutting a slice of a material, comprising a cradle (Bc) on which at least one double-acting hydraulic cylinder (V) coupled to a corresponding saw (Sc) is mounted, characterised in that it comprises a pair of valves (Ev1, Ev4) connected in a parallel assembly, by means of a first hydraulic circuit (1), to the upstream chamber (Cm) of the cylinder (V), and another pair of valves (Ev2, Ev3) connected in a parallel assembly, by means of a second hydraulic circuit (2), to the downstream chamber (Ca) of the cylinder (V), or vice versa. During operation, i.e. when the cradle is moved in a material, the sawing system can, as such, cut a slice of the material, for example in a silo, relatively quickly, by simultaneously switching the two pairs of valves.