Background: Nickel stannate nanocomposites could be useful for removing organic and toxic water pollutants, such as methyl orange (MO). Aim: The synthesis of a nickel oxide–tin oxide nanocomposite (NiO-SnO2 NC) via a facile and economically viable approach using a leaf extract from Ficus elastica for the photocatalytic degradation of MO. Methods: The phase composition, crystallinity, and purity were examined by X-ray diffraction (XRD). The particles’ morphology was studied using scanning electron microscopy (SEM). The elemental analysis and colored mapping were carried out via energy dispersive X-ray (EDX). The functional groups were identified by Fourier transform infrared spectroscopy (FTIR). UV–visible diffuse reflectance spectroscopy (UV–vis DRS) was used to study the optical properties such as the absorption edges and energy band gap, an important feature of semiconductors to determine photocatalytic applications. The photocatalytic activity of the NiO-SnO2 NC was evaluated by monitoring the degradation of MO in aqueous solution under irradiation with full light spectrum. The effects of calcination temperature, pH, initial MO concentration, and catalyst dose were all assessed to understand and optimize the physicochemical and photocatalytic properties of NiO-SnO2 NC. Results: NiO-SnO2 NC was successfully synthesized via a biological route using F. elastica leaf extract. XRD showed rhombohedral NiO and tetragonal SnO2 nanostructures and the amorphous nature of NiO-SnO2 NC. Its degree of crystallinity, crystallite size, and stability increased with increased calcination temperature. SEM depicted significant morphological changes with elevating calcination temperatures, which are attributed to the phase conversion from amorphous to crystalline. The elemental analysis and colored mapping show the formation of highly pure NiO-SnO2 NC. FTIR revealed a decrease in OH, and the ratio of oxygen vacancies at the surface of the NC can be explained by a loss of its hydrophilicity at increased temperatures. All the NC samples displayed significant absorption in the visible region, and a blue shift is seen and the energy band gap decreases when increasing the calcination temperatures due to the dehydration and formation of compacted large particles. NiO-SnO2 NC degrades MO, and the photocatalytic performance decreased with increasing calcination temperature due to an increase in the crystallite size of the NC. The optimal conditions for the efficient NC-mediated photocatalysis of MO are 100 °C, 20 mg catalyst, 50 ppm MO, and pH 6. Conclusions: The auspicious performance of the NiO-SnO2 NCs may open a new avenue for the development of semiconducting p–n heterojunction catalysts as promising structures for removing undesirable organic pollutants from the environment.