In recent years, the usages of by-products and wastes in industry have become more important. The importance of the sustainable development is also of increasing. The utilizations of wastes, as mineral admixture or fine aggregate, reduce the consumption of the natural resources and improve the durability of concrete. In this study, the effect of the fineness on the high temperature and sulphate resistances of concrete mortar specimens, produced with ground granulated blast-furnace slag (GBFS) replacing cement, is investigated. The compressive and flexural strength test results for all series related to durability effects, exposing temperature and solutions, exposure times for these durability effects, slag content and fineness are discussed. Consequently, the optimum slag contents are determined for producing the sulphate and high temperature resistant mortars.