Ethanol production by fermentation results in obtaining, in addition to the main product, ethyl alcohol, by-products and secondary products, which include carbon dioxide, fusel oil, and ester–aldehyde cut. Fusel oil, despite its low yield and the large volume of ethanol production, accumulates at distilleries, which ultimately raises the question of its disposal or the rational use of this by-product. Fusel oil, being a complex mixture, can serve as a source of technical alcohols used in various sectors of the economy, including the food industry, pharmaceuticals, organic synthesis, perfume, and cosmetics industries, as well as the production of paints and varnishes. However, the complexity of using fusel oil lies in its difficult separation. The reason for this is the presence of water, which forms low-boiling azeotropes with aliphatic alcohols. Our study aimed to develop a process flow diagram (PFD) that allows individual components from fusel oil to be obtained without extraneous separating agents (not inherent in fusel oil). This condition is necessary to obtain products labeled as natural for further use in the food, perfume, cosmetic, and pharmaceutical industries. The distinctive feature of this work is that the target product is not only isoamyl alcohol but also all other alcohols present in the composition of fusel oil. To achieve this goal and create a mathematical model, the Aspen Plus V14 application, the Non-Random Two Liquid (NRTL) thermodynamic model, and the Vap-Liq/Liq-Liq phase equilibrium were used. Fusel oil separation was modeled using a continuous separation PFD to obtain ethanol, water, isoamyl alcohol, and raw propanol and butanol cuts. The Sorel and Barbet distillation technique was used to isolate ethanol. The isolation of isopropanol and 1-propanol, as well as isobutanol and 1-butanol, was modeled using the batch distillation method. The isolation of fusel oil components was based on their thermodynamic properties and the selection of appropriate techniques for their separation, such as extraction, distillation, pressure swing distillation, and decantation. The simulation of fusel oil separation PFD showed the possibility of obtaining the components of a complex mixture without separating agents, as discussed earlier. Ethanol corresponds to the quality of rectified ethyl alcohol, and 1-butanol and isoamyl alcohols to anhydrous alcohols, whereas isopropanol (which contains an admixture of ethanol), 1-propanol, and isobutanol are obtained as aqueous solutions of different concentrations of alcohols. However, due to a distillation boundary in the raw propanol and butanol cuts, these mixtures cannot be separated completely, which leads to the production of intermediate fractions. To eliminate intermediate fractions and obtain anhydrous isopropanol, 1-propanol, and isobutanol in the future, it is necessary to solve the dehydration problem of either fusel oil or the propanol–butanol mixture.