The problem of spreading harmful infections through contaminated surfaces has become more acute during the recent coronavirus pandemic. The design of self-cleaning materials, which can continuously decompose biological contaminants, is an urgent task for environmental protection and human health care. In this study, the surface of blended cotton/polyester fabric was functionalized with N-doped TiO (TiO-N) nanoparticles using titanium(IV) isopropoxide as a binder to form durable photoactive coating and additionally decorated with Cu species to promote its self-cleaning properties. The photocatalytic ability of the material with photoactive coating was investigated in oxidation of acetone vapor, degradation of deoxyribonucleic acid (DNA) fragments of various lengths, and inactivation of PA136 bacteriophage virus and fungi under visible light and ultraviolet A (UVA) radiation. The kinetic aspects of inactivation and degradation processes were studied using the methods of infrared (IR) spectroscopy, polymerase chain reaction (PCR), double-layer plaque assay, and ten-fold dilution. The results of experiments showed that the textile fabric modified with TiO-N photocatalyst exhibited photoinduced self-cleaning properties and provided efficient degradation of all studied contaminants under exposure to both UVA and visible light. Additional modification of the material with Cu species substantially improved its self-cleaning properties, even in the absence of light.