Biodegradable and biocompatible 3D printable biomaterials with tunable mechanical properties and degradation rate adapted to target tissues were urgently required to manufacture scaffolds for tissue regeneration. Herein, a strategy based on a series of copolymers are proposed where the mechanical and degradation properties can be optimized regarding the specific biological application. With this purpose, poly(ɛ-caprolactone)-poly(ethylene glycol)-poly(ɛ-caprolactone) (PCL-PEG-PCL, PCEC) triblock co-polymers with high molecular weight were synthesized by using PEG with a wide range of molecular weight (from 0.6 kg/mol to 35 kg/mol) as macroinitiators. PCEC copolymers exhibited tunable mechanical properties with an elastic modulus in the range 338–705 MPa and a degradation rate from 60% mass loss after 8 h to 70% mass loss after 23 days in accelerated tests, as well as excellent cytocompatibility and cell attachment after culture with mouse fibroblast L929 cells. The mechanisms responsible for these properties were ascertained by means of different techniques to ascertain the structure–property relationship in PCEC copolymers. Furthermore, it was shown that it is possible to manufacture PCEC scaffolds by 3D printing with excellent dimensional accuracy and controlled microporosity. This study provides a promising strategy to design, select, and fabricate copolymers with tunable mechanical properties and degradation rate for tissue engineering applications.