A well-defined α,ω-dialdehyde polyisoprene-b-polystyrene block copolymer, synthesized using anionic polymerization high-vacuum techniques, is employed to prepare vitrimers with tris(2-aminoethyl)amine as the cross-linking agent. The vitrimer network, featuring dynamic imine cross-links, results in robust, flexible, and solvent-resistant films, which are applicable in thin film composite membranes. These vitrimer membranes, with molecular weight cut-offs in the nanofiltration range, are successfully used for organic solvent separation and evaluated for gas separation. The cross-linking density, controlled by the cross-linker, affects the material's gas permeability and affinity for CO₂. The dynamic nature of the imine cross-links enables the vitrimer's self-healing ability, activated by heat treatment at temperatures as low as 50 °C. Additionally, the vitrimer membranes can be reprocessed through solvent dissolution in the presence of the excess cross-linking agent.