This study investigated the release characteristics of curcumin (CUR)-loaded switchable poly(methyl methacrylate)-co-poly(N, N-Diethylaminoethyl methacrylate) (PMMA-co-PDEAEMA) membranes following the application of various stimuli, as well as the platform’s applicability in wound dressing and tissue engineering applications. The free-radical polymerization method was used to synthesize the PMMA-co-PDEAEMA copolymer. The drug-loaded nanofibrous membrane with electric potential (EP)-, CO2-, and pH-responsive properties was developed by the electrospinning of PMMA-co-PDEAEMA and CUR. The resulted structure was characterized by a scanning electron microscope (SEM) coupled with X-ray energy dispersive spectroscopy and wide-angle X-ray scattering measurements. The release characteristics of the CUR-loaded wound covering were analyzed in various simulated environments at varying voltages, alternated CO2/N2 gas bubbling, and at two different pH values; the results demonstrated high drug release controllability. Loaded CUR displayed high stability and better solubility compared with free CUR. The CUR-loaded tissue also exhibited high antibacterial activity against Escherichia coli and staphylococcus aureus bacteria. In addition, the MTT assay depicted high biocompatibility of up to 95% in the CUR-loaded membrane. This platform could be a promising candidate for usage in tissue engineering and medical applications such as targeted drug delivery, biodetection, reversible cell capture-and-release systems, and biosensors.