An abrasivejet cutting head is disclosed that includes a valve assembly for preventing back-flow to the abrasive hopper of abrasive-laden fluid from the cutting head when the discharge path for the abrasivejet becomes clogged or otherwise blocked. The valve assembly is positioned within the abrasive line to conduct abrasive from the hopper towards the abrasivejet nozzle. The valve assembly further includes a discharge path which is sealed off from the abrasivejet nozzle during normal operation in response to the relatively lower pressure in the abrasive jet nozzle that results from the flowing fluid therein. If the jet path is blocked or competed in a manner that causes a backflow of the abrasive-laden slurry therein, the cessation of low pressure permits the backflowing slurry to exit via the discharge path and bypass the hopper, substantially avoiding the downtime previously required to clean the hopper.