Atomic rearrangements within crystals lie at the foundation of electron-phonon-coupled phenomena such as metal-insulator transition and superconductivity. Advanced laser-pump-probe studies have recently focused on various charge-density-wave (CDW) materials to sharpen our understanding of the charge-lattice entanglement, where non-thermal melting of the CDW state is evident from the enhanced Bragg diffraction peak intensities - attributed to the dominance of the metal-atom dynamics over the nonmetal-anion one. Here using ultrafast MeV electron diffraction on the prototypical CDW material 1T-TaSeTe, we observe an unusual coexistence of systematically enhanced and suppressed Bragg peak intensities upon the CDW suppression, indicating a dominance of nonmetal-anion dynamics during photoexcitation. By tracking these atomic trajectories quantitatively through the ultrafast process, we identify a transient state that manifests itself as an unexpected decoupling of the Ta and Se/Te sublattices. These findings unambiguously unveil a new kind of laser manipulations of lattice order parameters, which has potentials in creating new quantum states and discerning hidden phases such as intra-unit-cell orders.