This study investigated the effect of water-washed municipal solid waste incineration fly ash (MSWI FA) as an admixture on the performance of dry mixed mortar and used X-ray diffraction (XRD) and scanning electron microscope (SEM) detection methods to conduct microscopic analysis. The experiment investigated the effects of the amount and water content of washed municipal solid waste incineration fly ash, cement, additives, sand and gravel, and curing time on the compressive flexural strength of dry mixed mortar at 28 days. The results show that when the content of water-washed MSWI FA is 9.80%, the content of sand and gravel is 73.50%, the content of ordinary Portland cement (PO42.5) is 16.66%, the content of water-reducing agent is 1.47‰, the content of cellulose is 0.03‰, the content of the expansion agent is 0.49‰, the addition of water is 130–160 mL/kg, the consistency of the sample can reach 91.8 mm, and the water retention rate can reach 93.6%. The flexural strength of the sample at 28 days can reach 7.5 MPa, and the compressive strength at 28 days can reach 28.30 MPa. Metal ions, such as Pb2+ and Gd2+ in MSWI FA, under the combined action of silicate cement in dry mixed mortar and fibers in cellulose, crisscross and form a solidified material, which will not be leached out. This quality meets the requirements of dry mixed mortar for ordinary plastering and masonry mortar (GB-T 25181-2019), and the leaching toxicity of the sample meets the “Identification Standard for Hazardous Waste” (GB5085.3-2007). This work provides a meaningful exploration of the resource utilization of water-washed MSWI FA.