Thermally induced phase separation followed by freeze drying has been used to prepare biodegradable and biocompatible scaffolds with interconnected 3D microporous structures from poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) copolymers containing 5 and 12 wt % of 3-hydroxyvalerate (HV). Solutions of PHBV in 1,4-dioxane, underwent phase separation by cooling under two different thermal gradients (at −25◦ C and −5◦ C). The cloud point and crystallization temperature of the polymer solutions were determined by turbidimetry and differential scanning calorimetry, respectively. Parameters affecting the phase separation mechanism such as variation of both the cooling process and the composition of the PHBV copolymer were investigated. Afterwards, the influence of these variables on the morphology of the porous structure and the final mechanical properties (i.e., rigidity and damping) was evaluated via scanning electron microscopy and dynamic mechanical thermal analysis, respectively. While the morphology of the scaffolds was considerably affected by polymer crystallization upon a slow cooling rate, the effect of solvent crystallization was more evident at either high hydroxyvalerate content (i.e., 12 wt % of HV) or high cooling rate. The decrease in the HV content gave rise to scaffolds with greater stiffness because of their higher degree of crystallinity, being also noticeable the greater consistency of the structure attained when the cooling rate was higher. Scaffolds were fully biocompatible supports for cell adhesion and proliferation in 3D cultures and show potential application as a tool for tissue regeneration.