We report biodegradable thermoplastic polyurethanes for soft tissue engineering applications, where frequently used carboxylic acid ester degradation motifs were substituted with carbonate moieties to achieve superior degradation properties. While the use of carbonates in soft blocks has been reported, their use in hard blocks of thermoplastic polyurethanes is unprecedented. Soft blocks consist of poly(hexamethylene carbonate), and hard blocks combine hexamethylene diisocyanate with the newly synthesized cleavable carbonate chain extender bis(3-hydroxypropylene)carbonate (BHPC), mimicking the motif of poly(trimethylene carbonate) with highly regarded degradation properties. Simultaneously, the mechanical benefits of segmented polyurethanes are exploited. A lower hard block concentration in BHPC-based polymers was more suitable for vascular grafts. Nonacidic degradation products and hard block dependent degradation rates were found. Implantation of BHPC-based electrospun degradable vascular prostheses in a small animal model revealed high patency rates and no signs of aneurysm formations. Specific vascular graft remodeling and only minimal signs of inflammatory reactions were observed.