In this study, the impact response of sandwich panels incorporating a date-palm wood core was experimentally investigated under low-velocity perforation loading. Six panel configurations were manufactured using two core thicknesses (20 and 40 mm) and three impact energy levels (50, 100, and 150 J). Perforation tests were carried out with a 10-kg drop-weight impactor. Force–displacement curves and absorbed-energy histories were extracted, and the failure mechanisms were examined by comparing the front- and back-face damage patterns. The results showed that the heterogeneous cellular architecture of date-palm wood produces a multi-stage energy-absorption response, resulting in complete perforation accompanied by progressive core crushing at all investigated energy levels. Increasing the core thickness markedly improved the energy-absorption capacity; the absorbed energy of the 40-mm specimens under the 100-J impact was more than three times that of the 50-J specimens. Additionally, the peak force increased from about 2.3 kN at 50 J to over 6.3 kN at 150 J. Failure analysis revealed a combined mechanism involving face-sheet punching, cellular core crushing, and plug pull-out on the back face. Higher impact energies were associated with reduced energy-absorption efficiency due to the greater contribution of brittle fracture and full perforation. Overall, the findings demonstrate that date-palm wood is a promising bio-based core material with favorable mechanical characteristics for energy-absorption applications in sandwich structures.