Exposure of concrete to acidic environments can cause the degradation of concrete elements and seriously affect the durability of concrete. As solid wastes are produced during industrial activity, ITP (iron tailing powder), FA (fly ash), and LS (lithium slag) can be used as admixtures to produce concrete and improve its workability. This paper focuses on the preparation of concrete using a ternary mineral admixture system consisting of ITP, FA, and LS to investigate the acid erosion resistance of concrete in acetic acid solution at different cement replacement rates and different water–binder ratios. The tests were performed by compressive strength analysis, mass analysis, apparent deterioration analysis, and microstructure analysis by mercury intrusion porosimetry and scanning electron microscopy. The results show that when the water–binder ratio is certain and the cement replacement rate is greater than 16%; especially at 20%, the concrete shows strong resistance to acid erosion; when the cement replacement rate is certain and the water–binder ratio is less than 0.47; especially at 0.42, the concrete shows strong resistance to acid erosion. Microstructural analysis shows that the ternary mineral admixture system composed of ITP, FA, and LS promotes the formation of hydration products such as C-S-H and AFt, improves the compactness and compressive strength of concrete, and reduces the connected porosity of concrete, which can obtain good overall performance. In general, concrete prepared with a ternary mineral admixture system consisting of ITP, FA, and LS has better acid erosion resistance than ordinary concrete. The use of different kinds of solid waste powder to replace cement can effectively reduce carbon emissions and protect the environment.