Degradable shape-memory polymers are multifunctional materials with broad applicability for medical devices. They are designed to acquire their therapeutically relevant shape and mechanical properties after implantation. In this study, the potential of a completely amorphous shape-memory polymer matrix for controlled drug release was comprehensively characterized according to a four step general strategy which provides concepts for validating multifunctional materials for pharmaceutical applications. Independent functionalities are thereby crucial for fully exploiting the potential of the materials. The copolyester urethane network was synthesized by crosslinking star-shaped tetrahydroxy telechelics of oligo[(rac-lactide)-co-glycolide] with an aliphatic diisocyanate. In step 1 of the four step characterization procedure, this material showed the thermal and mechanical properties, which are required for the shape-memory effect under physiological conditions. Shape recovery could be realized by a one-step or a multi-step methodology. In step 2, feasibility of drug loading of pre-formed shape-memory networks has been demonstrated with drugs of different hydrophobicities. The presence of drugs did not disturb the material's functionalities directly after loading (step 3) and under release conditions (step 4). A predictable release of about 90% of the payload in 80 days was observed. Overall, the synthesized amorphous polymer network showed three independent functionalities, i.e., a shape-memory effect combined with biodegradability and controlled drug release.