Solids irradiated by energetic photons can be eroded in two modes, depending on the radiation intensity. High average, low-peak power sources, e.g., synchrotron radiation and high-order harmonics, induce desorption of the material at a low etch rate. In contrast, high-peak-power radiation from extreme ultraviolet and x-ray lasers usually causes a massive removal of the material even by a single shot. In this contribution, an effective material erosion is reported in PMMA exposed to multiple accumulated pulses generated by the free-electron x-ray-laser Linac Coherent Light Source (LCLS, tuned at a photon energy of 830 eV in this study, operated in Menlo Park at Stanford, CA, USA) at a fluence below the single-pulse ablation threshold. The effect is caused by polymer-chain scissions initiated by single photons carrying enough energy to break the $\mathrm{C}---\mathrm{C}$ bounds. High efficiency of the erosion is supposed to occur due to a correlation of the single-photon effects. The subthreshold damage exhibits a nonlinear dose dependence resulting from a competition between chain scissions and cross-linking processes. The cross-linking is proven by Raman spectroscopy of the irradiated polymer. Two theoretical models of the x-ray free-electron-laser-induced erosion are suggested, which provide an excellent agreement with the experimental results.