Ammonia, as an alternative fuel for internal combustion engines, can achieve nearly zero carbon emissions. Although the development of the pure ammonia engine is limited by its poor combustion characteristics, ammonia–hydrocarbon mixed combustion can effectively improve the combustion of ammonia fuel. With the increase in the ammonia fuel proportion in the fuel mixture, a large number of nitrogen oxides (NOX) and unburned ammonia may be discharged, which have a poor impact on the environment. In this study, the performance of selective catalytic reduction (SCR) aftertreatment technology in reducing NOX and ammonia emissions from ammonia–diesel dual-fuel engines was investigated using simulation. A good cross-dimensional model was established under the coupling effect, though the effect of a single-dimensional model could not be presented. The results show that when the exhaust gas in the engine cylinder is directly introduced into the SCR without additional reducing agents such as urea, unburned ammonia flowing into SCR model is in excess, and there will be only ammonia at the outlet; however, if the unburned ammonia fed into the SCR model is insufficient to reduce NO, the ammonia concentration at the outlet will be 0. NOX can be 100% effectively reduced to N2 under most engine conditions; thus, unburned ammonia in exhaust plays a role in reducing NOX emissions from ammonia–diesel dual-fuel engines. However, when the concentration of unburned ammonia in the exhaust gas of an ammonia–diesel dual-fuel engine is large, its ammonia emissions are still high even after the SCR. In addition, the concentrations of N2O after SCR do not decrease, but increase by 50.64 in some conditions, the main reason for which is that by the action of the SCR catalyst, NO2 is partially converted into N2O, resulting in an increase in its concentration at the SCR outlet. Adding excessive air or oxygen into the SCR aftertreatment model can not only significantly reduce the ammonia concentration at the outlet of the model without affecting the NOX conversion efficiency of SCR, but inhibit N2O production to some extent at the outlet, thus reducing the unburned ammonia and NOX emissions in the tail gas of ammonia–diesel dual-fuel engines at the same time without the urea injection. Therefore, this study can provide theoretical guidance for the design of ammonia and its mixed-fuel engine aftertreatment device, and provide technical support for reducing NOX emissions of ammonia and its mixed fuel engines.