The invention relates to a method for co-producing manganese hydroxide and sulfuric acid or ammonium sulfite with electrolytic manganese waste slag, comprising the following steps: A. slurrying electrolytic manganese metal waste slag, leaching, adjusting pH to 6.0-6.4, removing iron, and pressing filtration to obtain Press filter block A and press filter liquid A, press filter press block A after water washing, obtain press filter block B and press filter liquid B; Regulate the pH of press filter liquid A to 11.5-12, press filter, obtain press filter block C and press filter liquid C, press filtrate C circulation treatment, after potassium and sodium enrichment, remove calcium sulfate, evaporate and crystallize, separate potassium sulfate and sodium sulfate; B. calculate according to production needs and add the required substances to the press block B, dry Drying, pre-decomposition, and calcination to obtain cement additives or solids. The sulfur dioxide produced by calcination is separated from the dedusting ash for powder gas separation. The sulfur dioxide gas is used to make sulfuric acid. The dedusting ash and filter press block B are calcined together to enrich selenium and zinc; C. Slurry the filter block C, leaching, adjust the pH to 6.0-6.4, remove impurities, stand still, and press filter to obtain the filter block D and the filter liquid D, adjust the pH of the filter liquid D to 8.8-9, and continue to adjust the solution pH to 11.4‑11.8. This method realizes the joint output of multiple products.