The homopolymer poly(butylene succinate) (PBS) and its copolymers containing 1,4-cyclohexane dimethylene succinate (CHDMS) or butylene 1,4-cyclohexanedicarboxylate (BCHDA) sequences with different molecular architectures (P(BS-co-CHDMS) and P(BS-co-BCHDA)) were prepared via melt polycondensation in the presence of a Ti-based catalyst. With the aim to gain more underlying information about enzymatic degradation rules and differences, the enzymatic degradation studies were performed in chloroform using Pseudomonas cepacia lipase (PCL) for 60 h. Degradation was monitored using various analytical techniques such as GPC, TGA and MALDI-TOF-MS. The results show that all PBS-based copolymers had an obvious degradation in chloroform. Compared with P(BS-co-BCHDA), P(BS-co-CHDMS) showed greater degradation rates after 60 hours of enzymatic degradation. The maximum degradation percentage observed in P(BS-co-10%CHDMS) was about 85%. Similarly, thermal property changes were observed with a decrease of the decomposition temperature of 5% and 15% sample in most cases. The enzymatic degradation of PBS-based copolymers produced not only linear segments, but also cyclic oligomers. Furthermore, P(BS-co-CHDMS) produced more oligomers than PBS-co-BCHDA. According to the results of molecular docking, the free energy of binding between PCL and the substrate in chloroform was in the order CMSCM > BSCM > BCAB > BSB. That is, the docking of the substrate containing CHDMS in the active site of PCL was more stable than any other ones.