Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photodissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, which affects planet formation within the disks. We report James Webb Space Telescope and Atacama Large Millimeter Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modeling their kinematics and excitation allowed us to constrain the physical conditions within the gas. We quantified the mass-loss rate induced by the FUV irradiation and found that it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk.