An abrasive water-jet cutting machine, comprising: - pumping means, fluidically connectable to a water source, for the generation of a pressurized water flow; - a cutting head, comprising a primary nozzle, a mixing chamber and a focusing nozzle, wherein the pressurized water flow originating from the pumping means is conveyed into the primary nozzle of the cutting head where the pressure energy of the pressurized water flow is converted into kinetic energy so as to form a water jet, and wherein said water jet is then conveyed into the mixing chamber; - a dispensing system of powdered abrasive material, comprising: - a tank containing powdered abrasive material, - a feeding pipe, fluidically connecting the tank to the mixing chamber of the cutting head, - a dispenser, dispensing the powdered abrasive material contained within the tank into the mixing chamber by means of the feeding pipe; wherein the cutting head mixes, in the mixing chamber, the abrasive material with the water jet forming a water-abrasive material mixture jet, and said cutting head dispenses the water-abrasive material mixture jet by means of the focusing nozzle; wherein the powdered abrasive material contained in the tank is homogeneously dispersed in suspension in a gelatinous water-based fluid; characterised in that the mass ratio of the dispersed powdered abrasive material to the gelatinous water-based fluid is from 1.0 to 3.5. - pumping means, fluidically connectable to a water source, for the generation of a pressurized water flow; - a cutting head, comprising a primary nozzle, a mixing chamber and a focusing nozzle, wherein the pressurized water flow originating from the pumping means is conveyed into the primary nozzle of the cutting head where the pressure energy of the pressurized water flow is converted into kinetic energy so as to form a water jet, and wherein said water jet is then conveyed into the mixing chamber; - a dispensing system of powdered abrasive material, comprising: - a tank containing powdered abrasive material, - a feeding pipe, fluidically connecting the tank to the mixing chamber of the cutting head, - a dispenser, dispensing the powdered abrasive material contained within the tank into the mixing chamber by means of the feeding pipe; wherein the cutting head mixes, in the mixing chamber, the abrasive material with the water jet forming a water-abrasive material mixture jet, and said cutting head dispenses the water-abrasive material mixture jet by means of the focusing nozzle; wherein the powdered abrasive material contained in the tank is homogeneously dispersed in suspension in a gelatinous water-based fluid; characterised in that the mass ratio of the dispersed powdered abrasive material to the gelatinous water-based fluid is from 1.0 to 3.5. - a tank containing powdered abrasive material, - a feeding pipe, fluidically connecting the tank to the mixing chamber of the cutting head, - a dispenser, dispensing the powdered abrasive material contained within the tank into the mixing chamber by means of the feeding pipe; wherein the cutting head mixes, in the mixing chamber, the abrasive material with the water jet forming a water-abrasive material mixture jet, and said cutting head dispenses the water-abrasive material mixture jet by means of the focusing nozzle; wherein the powdered abrasive material contained in the tank is homogeneously dispersed in suspension in a gelatinous water-based fluid; characterised in that the mass ratio of the dispersed powdered abrasive material to the gelatinous water-based fluid is from 1.0 to 3.5.