A series of environmentally-friendly bio-based poly(1,3-propylene succinate) diols (bio-PPS) with different average molecular weights (Mn) were synthesized from bio-based 1,3-propanediol (bio-PDO) and bio-based succinic acid (bio-SA). With the employment of bio-PPS as a hydrophobic block and poly(ethylene glycol) (PEG) as a hydrophilic segment, the well-defined amphiphilic triblock and multi-block polyurethane (PU) copolymers with the urethane linkages between the blocks were synthesized and characterized. The chemical structures and molecular weights of these block PU copolymers were confirmed by proton nuclear magnetic resonance (1H NMR), Fourier transform infrared (FT-IR) spectrum, differential scanning calorimetry (DSC), and gel permeation chromatography (GPC). With the Mn of bio-PPS blocks increasing from 1.40 to 8.93 kg/mol, the degree of hydrogen bonding in the PUs reduced significantly, and the glass transition temperature increased from −42.8 to −35.4 °C and from −40.1 to −33.1 °C for triblock and multi-block copolymers, respectively. Transmission electron microscopy (TEM) images revealed that both triblock and multi-block PU copolymers could spontaneously self-assemble into near-spherical core-shell micelles in aqueous solution. With the increasing bio-PPS content in the copolymers, the sizes of triblock micelles from dynamic light scattering (DLS) measurement varied from 17 to 64 nm, and the critical micelle concentration (CMC) changed from 7.22 to 0.77 mg/L. For the multi-block series, the micelle sizes increased from 24 to 71 nm and the CMC values decreased from 2.85 to 1.79 mg/L. The enzymatic degradation of the micelles for 8 weeks under the physiological environment revealed that hydrophilic PEG segments could be detached from the main chain of triblock micelles, and the degradation mainly occurred at the ester group of bio-PPS blocks in the multi-block ones. Micelles with lower bio-PPS content and multi-block architecture degraded faster during the enzymatic degradation process. A controlled release profile was observed for the doxorubicin (DOX)-loaded micelles, more than 40% and 50% DOX were released after 75 h from triblock and multi-block micelles, respectively. Moreover, the addition of lipase could accelerate the DOX release from the micelles. Cytotoxicity test proved that the PU micelles were nontoxic, while the DOX loaded micelles showed concentration-dependent cytotoxicity to HeLa cells, suggesting its potential application in the drug delivery system.