An abrasive water jet processing machine for jetting a fluid and performing a cutting includes a fluid supply device, an abrasive supply device, an injection pressure controller, wherein the abrasive supply device includes a reservoir hopper consisting of a pressure vessel for reserving the abrasive, an abrasive supply tube for communicating with the reservoir hopper and the nozzle, and an air purge device for supplying compressed air to the abrasive supply tube and the reservoir hopper; the injection pressure controller performs a two-stage control of controlling injection pressure in a piercing; and the air purge device includes a flow pressure controller for controlling flow pressure of compressed air passing through the abrasive supply tube, wherein the flow pressure controller controls the flow pressure in the piercing to be higher than that in the cutting.