We study the response of a radiation-amorphized material to high pressure. We have used zircon ZrSiO4 amorphized by natural radiation over geologic times, and have measured its volume under high pressure, using the precise strain-gauge technique. On pressure increase, we observe apparent softening of the material, starting from 4 GPa. Using molecular dynamics simulation, we associate this softening with the amorphous-amorphous transformation accompanied by the increase of local coordination numbers. We observe permanent densification of the quenched sample and a nontrivial "pressure window" at high temperature. These features point to a new class of amorphous materials that show a response to pressure which is distinctly different from that of crystals.