Selecting the right polymer–modifier pairs is essential for creating mixed matrix membranes (MMMs) with enhanced transport properties. In this study, novel dense and supported MMMs based on the biopolymer carboxymethylcellulose (CMC) modified using Cu-based metal–organic frameworks (MOFs: HKUST-1 and HKUST-1-AcOH) were developed to improve the pervaporation dehydration of isopropanol. The effect of varying the content of the MOFs, selecting the solvent for creating of polyacrylonitrile (PAN)-based porous support, and choosing the concentration of the CMC solution for developing supported membranes on the structure and properties was investigated. The synthesized MOFs and CMC-based membranes were studied using Fourier–transform infrared spectroscopy, X-ray diffraction analysis, surface area measurement, scanning electron microscopy, atomic force microscopy, energy- dispersive X-ray spectroscopy, thermogravimetric analysis, contact angle, mechanical properties, and swelling measurements. The transport properties of dense and supported membranes were tested in the pervaporation dehydration of isopropanol. Combining a 10 wt.% HKUST-1-AcOH concentration, a porous PAN support, a 0.5 wt.% CMC concentration, and cross-linking the polymer chains with glutaraldehyde (GA) resulted in a membrane that remained stable for 8 days and exhibited improved performance, achieving the highest permeation flux (0.075–1.264 kg/(m2 h)), pervaporation separation index (≥ 123 kg/(m2 h)), and component permeances (≥ 2123 GPU for water and ≥ 0.28 GPU for isopropanol) in the pervaporation separation of water/isopropanol mixtures containing 12–90 wt.% water at 22 °C.