Polydepsipeptides, alternating copolymers consisting of α-amino acids and α-hydroxy acids, are degradable polymers. Depsipeptide-based polymers of varied architectures can be synthesized via ring-opening polymerization of various morpholine-2,5-dione derivatives. Thermoplastic phase-segregated multiblock copolymers with poly(ε-caprolactone) (PCL) and poly(iso-butyl-morpholinedione) segments have been synthesized from the macrodiols and an aliphatic diisocyanate as a coupling agent. The respective multiblock copolymers showed shape-memory capabilities and good elastic properties, making them attractive candidates for potential application as biomaterials for controlled drug release systems, scaffolds to be applied in tissue engineering or biofunctional implants. Thus, these abilities cumulate to form multifunctional materials, combining degradability with shape-memory capability. The advantages of depsipeptide-based multiblock copolymers compared to previously reported poly(ether)ester-derived biomaterials having shape-memory property may result from their different degradation products, as the resulting α-amino acids may act as a buffer for the hydroxy acids, thereby stabilizing pH values. In this context, we report on the biological evaluation of material samples in accordance with international standards (EN DIN ISO 10993-5 and 10993-12). Here, extracts of the substrates were exposed to a continuous fibroblast like cell line (L929) to study cytocompatibility of extractable substrates. Cell viability, morphology, LDH-release (as a parameter for the functional integrity of the cell membrane), activity of the mitochondrial dehydrogenases (as a parameter of the cell activity) and assembly of the actin- and vinculin cytoskeleton indicated no incompatibilities between the extracts and L929 cells. These results suggest that depsipeptide-based multiblock copolymers are promising candidates for soft, multifunctional implant materials.