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Charge order (CO) is ubiquitous in the high-T_c cuprates but its relation to superconductivity is still unclear. While static charge order seems to anticorrelate with superconductivity, charge order fluctuations may favor or enhance Cooper pairing. Here, we investigate the collective CO dynamics in the prototypical cuprate La_2-xBa_xCuO₄ with time-resolved resonant soft x-ray scattering. By suddenly quenching the CO diffraction peak with ultrafast optical pump pulses and probing its recovery in the time domain with resonant soft x-rays, we find that CO excitations in the energy range 0.4-2.0 meV are overdamped and diffusive. At energy scales lower than 0.4 meV, the CO phase exhibits dynamical critical scaling, a universal behavior associated with the propagation of topological defects. Our observations imply that charge order is dynamic and may play a role in establishing superconducting pairing.