The functional differences between invasive plants and coexisting native plants can affect the invasion process of the former because invasive plants and coexisting native plants are exposed to similar or even identical environmental pressures. Acid deposition is an important component of atmospheric pollution, and acid deposition with different sulfur–nitrogen ratios may affect the invasion process of invasive plants by shifting the functional differences and differences in the growth performance between the invasive and coexisting native plants. It is crucial to analyze the functional indices and growth performance of these plants when exposed to acid deposition with different chemical compositions to assess the ecological impacts of atmospheric pollution on the growth performance of invasive plants. This study aimed to evaluate the functional differences and growth performance between the invasive plant Amaranthus spinosus L. and the native plant A. tricolor L. in mono- and mixed culture when exposed to an acid deposition with different sulfur–nitrogen ratios, including sulfur-rich acid deposition (sulfur–nitrogen ratio = 5:1), nitrogen-rich acid deposition (sulfur–nitrogen ratio = 1:5), and mixed acid deposition (sulfur–nitrogen ratio = 1:1). The acidity of the three types of simulated acid deposition was set at pH = 5.6 and pH = 4.5, respectively, with distilled water as a control (pH = 7.0). The competition experiment between A. spinosus and A. tricolor was conducted in the greenhouse. Amaranthus spinosus exhibited a strong growth performance over A. tricolor in the mixed culture, mainly via the increased leaf photosynthetic capacity. The competitiveness for light acquisition, leaf photosynthetic capacity, and enzymatic defense capacity under stress of A. spinosus may be vital to its growth performance. The lower pH acid deposition had imposed a greater reduction in the growth performance of both Amaranthus species than the higher pH acid deposition. Sulfur-rich acid deposition was more toxic to the growth performance of both Amaranthus species than nitrogen-rich acid deposition. Amaranthus spinosus was more competitive than A. tricolor, especially when exposed to acid deposition, compared with just distilled water. Thus, acid deposition, regardless of the sulfur–nitrogen ratio, may facilitate the invasion process of A. spinosus via the stronger growth performance.