This work deals with molecular mobility in renewable block copolymers based on polylactide (PLA) and poly(propylene adipate) (PPAd). In particular, we assess non-trivial effects on the mobility arising from the implementation of crystallization. Differential scanning calorimetry, polarized light microscopy and broadband dielectric spectroscopy were employed in combination for this study. The materials were subjected to various thermal treatments aiming at the manipulation of crystallization, namely, fast and slow cooling, isothermal melt- and cold-crystallization. Subsequently, we evaluated the changes recorded in the overall thermal behavior, semicrystalline morphology and molecular mobility (segmental and local). The molecular dynamics map for neat PPAd is presented here for the first time. Unexpectedly, the glass transition temperature, T_g, in the amorphous state drops upon crystallization by 8–50 K. The drop becomes stronger with the increase in the PPAd fraction. Compared to the amorphous state, crystallization leads to significantly faster segmental dynamics with severely suppressed cooperativity. For the PLA/PPAd copolymers, the effects are systematically stronger in the cold- as compared to the melt-crystallization, whereas the opposite happens for neat PLA. The local β_PLA relaxation of PLA was, interestingly, recorded to almost vanish upon crystallization. This suggests that the corresponding molecular groups (carbonyl) are strongly involved and immobilized within the semicrystalline regions. The overall results suggest the involvement of either spatial nanoconfinement imposed on the mobile chains within the inter-crystal amorphous areas and/or a crystallization-driven effect of nanophase separation. The latter phase separation seems to be at the origins of the significant discrepancy recorded between the calorimetric and dielectric recordings on T_g in the copolymers. Once again, compared to more conventional techniques such as calorimetry, dielectric spectroscopy was proved a powerful and quite sensitive tool in recording such effects as well as in providing indirect indications for the polymer chains’ topology.