Background: Biodegradable polyurethanes have found widespread use in soft tissue engineering due to their suitable mechanical properties and biocompatibility. Methods: In this study, polyurethane samples were synthesized from polycaprolactone, hexamethylene diisocyanate, and a copolymer of 1,4-butanediol as a chain extender. Polyurethane scaffolds were fabricated by a combination of liquid–liquid phase separation and salt leaching techniques. The effect of the NCO:OH ratio on porosity content and pore morphology was investigated. Results: Scanning electron micrographs demonstrated that the scaffolds had a regular distribution of interconnected pores, with pore diameters of 50–300 µm, and porosities of 64%–83%. It was observed that, by increasing the NCO:OH ratio, the average pore size, compressive strength, and compressive modulus increased. L929 fibroblast and chondrocytes were cultured on the scaffolds, and all samples exhibited suitable cell attachment and growth, with a high level of biocompatibility. Conclusion: These biodegradable polyurethane scaffolds demonstrate potential for soft tissue engineering applications.