New methods for the synthesis of aliphatic polyesters were proposed and realized with highly effective and low-toxic 1,5,7-triazabicyclo[4.4.0]decene-5 and (2,6-di-tert-butyl-4-methylphenoxy)-butyl-magnesium as catalysts and ethanol as an initiator. The interaction processes between D,L-polylactides of different molecular weights, obtained through these methods, and supercritical carbon dioxide were studied to provide “soft and dry” formation (without high temperatures and toxic organic solvents) of highly porous (up to 90 vol %) bioresorbable matrices for tissue engineering constructions. The chemical structure, molecular weight characteristics, morphology, cytotoxicity, and matrix properties of the samples synthesized from D,L-polylactides were studied with nuclear magnetic resonance spectroscopy, gel permeation chromatography, scanning electron microscopy, colorimetric testing to estimate the metabolic activity of cells (MTT test), and coloration with a vital fluorescent dye of in vitro cultures of multipotent stromal cells of human adipose tissue. A comparative analysis for biocompatibility of these matrices with control samples made from “medical grade” polylactide analog produced industrially indicates that the materials developed can be recommended for tissue engineering.