Salinity is one of the main environmental stresses, and it affects potato growth and productivity in arid and semiarid regions by disturbing physiological process, such as the photosynthesis rate, the absorption of essential nutrients and water, plant hormonal functions, and vital metabolic pathways. Few studies are available on the application of combined nanomaterials to mitigate salinity stress on potato plants (Solanum tuberosum L. cv. Diamont). In order to assess the effects of the sole or combined application of silicon (Si) and potassium (K) nanoparticles and biochar (Bc) on the agro-physiological properties and biochemical constituents of potato plants grown in saline soil, two open-field experiments were executed on a randomized complete block design (RCBD), with five replicates. The results show that the biochar application and nanoelements (n-K and n-Si) significantly improved the plant heights, the fresh and dry plant biomasses, the numbers of stems/plant, the leaf relative water content, the leaf chlorophyll content, the photosynthetic rate (Pn), the leaf stomatal conductance (Gc), and the tuber yields, compared to the untreated potato plants (CT). Moreover, the nanoelements and biochar improved the content of the endogenous elements of the plant tissues (N, P, K, Mg, Fe, Mn, and B), the leaf proline, and the leaf gibberellic acid (GA3), in addition to reducing the leaf abscisic acid content (ABA), the activity of catalase (CAT), and the peroxidase (POD) and polyphenol oxidase (PPO) in the leaves of salt-stressed potato plants. The combined treatment achieved maximum plant growth parameters, physiological parameters, and nutrient concentrations, and minimum transpiration rates (Tr), leaf abscisic acid content (ABA), and activities of the leaf antioxidant enzymes (CAT, POD, and PPO). Furthermore, the combined treatment also showed the highest tuber yield and tuber quality, including the contents of carbohydrates, proteins, and the endogenous nutrients of the tuber tissues (N, P, and K), and the lowest starch content. Moreover, Pearson’s correlation showed that the plant growth and the tuber yields of potato plants significantly and positively correlated with the photosynthesis rate, the internal CO2 concentration, the relative water content, the proline, the chlorophyll content, and the GA3, and that they were negatively correlated with the leaf Na content, PPO, CAT, ABA, MDA, and Tr. It might be concluded that nanoelement (n-K and n-Si) and biochar applications are a promising method to enhance the plant growth and crop productivity of potato plants grown under salinity conditions.