The influence of degradation on non-isothermal crystallization from the melt of a segmented copolymer constituted of glycolide and trimethylene carbonate units and used as a bioabsorbable surgical suture was studied by optical microscopy, differential scanning calorimetry and time-resolved X-ray diffraction. Fibrillar positive spherulites were obtained with slightly degraded samples but new axialitic morphologies were detected when samples had a molecular weight, Mw, lower than 29,000 g/mol and the crystallization started at a high temperature. Crystal growth kinetics of samples degraded under different conditions was evaluated over a wide temperature range by a non-isothermal method. Two crystallization regimes (I and II) were determined for the more degraded samples (i.e., those able to crystallize according to axialitic and spherulitic morphologies), whereas only regime II was found for samples of higher molecular weights. Primary nucleation density decreased with the extent of degradation provided no morphological changes occurred, and so did the regularity of lamellar stacking, as shown by synchrotron measurements, although the morphological parameters remained practically constant.