The present paper investigates the response a sandwich composite laminate that involves intraply hybrid carbon fiber reinforced polymer (CFRP)/Dyneema core under impact and post-impact tests. This intraply hybrid core was designed to gain the high elasticity and high stiffness/weight ratio of Dyneema fibers while maintaining the structural integrity of CFRP at the laminate core. Low-velocity impact and compression after impact tests were employed to evaluate the damage resistance and tolerance of the laminates. Microcomputed tomography was deployed to inspect the different modes of damage and their propagation during low-velocity impact. The results showed that the damage started in the sandwich composite as localized matrix cracks and delaminations at CFRP impacted face. However, it was distributed through the whole laminate thickness in the monolithic CFRP composites. The fiber cut initiated at 70 J impact energy for the sandwich composite at the impacted CFRP face plies as fiber kinking due to compressive stresses. However, it was initiated at the lower plies of the CFRP composite at 30 J due to high bending and normal strains. This delayed fiber breakage revealed the better residual compression after impact (CAI) strength of the sandwich composite, where it showed 33.5% improved specific CAI strength compared to the monolithic CFRP composite.