Acrylate-endcapped urethane-based precursors constituting a poly(D,L-lactide)/poly(ε-caprolactone) (PDLLA/PCL) random copolymer backbone are synthesized with linear and star-shaped architectures and various molar masses. It is shown that the glass transition and thus the actuation temperature could be tuned by varying the monomer content (0-8 wt% ε-caprolactone, Tg,crosslinked = 10-42 °C) in the polymers. The resulting polymers are analyzed for their physico-chemical properties and viscoelastic behavior (G'max = 9.6-750 kPa). The obtained polymers are subsequently crosslinked and their shape-memory properties are found to be excellent (Rr = 88-100%, Rf = 78-99.5%). Moreover, their potential toward processing via various additive manufacturing techniques (digital light processing, two-photon polymerization and direct powder extrusion) is evidenced with retention of their shape-memory effect. Additionally, all polymers are found to be biocompatible in direct contact in vitro cell assays using primary human foreskin fibroblasts (HFFs) through MTS assay (up to ≈100% metabolic activity relative to TCP) and live/dead staining (>70% viability).