The dynamic mechanical response and deformation mechanism of poly (ε-caprolactone) (PCL) and epoxy resins shape memory polymer (SMP) composites were investigated in this paper. The SMP composites were a blend of PCL and epoxy resins by using the facile melt-mixing method. The distribution of PCL in the composites was observed by SEM, which was in from microparticle morphology to continuous morphology with the increasing PCL content. And the dynamic mechanical analyzer (DMA) tests were performed to demonstrate the viscoelastic properties and shape memory effect of the PCL/EP composites. Based on the above characterization of PCL/EP composites, the split Hopkinson pressure bar (SHPB) tests were performed to study the dynamic mechanical properties at the strain rates of 4000/s to 7000/s. The results showed that the flow stress increased with the increasing strain rate, which exhibited an obvious sensitivity to strain rate. However, the flow stress of PCL/EP decreases with the increasing PCL content due to the low strength of PCL. And PCL/EP composites failed in a typical ductile failure mode under quasi-static loading, whereas an excellent plastic deformation ability was observed at high strain rates, which was attributed to the heat generated by the plastic work during the adiabatic compression. Combining with the experimental results, the corresponding deformation mechanism was also discussed.