Finding the solution to the problem of the accumulating waste from the mining and processing industries, as well as reducing their carbon footprint, is among the most important tasks today. Within the construction industry, in the field of the production of building materials such as concrete, these problems may be solved through the use of waste and by saving the binder component. The purpose of this study is to substantiate the feasibility of using waste coal dust (CD) in concrete and cement–sand mortars as a partial replacement for cement. Test samples were made by partially replacing cement with CD in an amount from 0% to 10% in increments of 2% by weight. The following main characteristics were studied: mobility and density of mixtures, as well as density, compressive strength, bending strength and water absorption of concrete and mortars. X-ray diffraction and microscopic analysis methods were used in this work. The introduction of CD to replace part of the cement, up to 10%, did not have a significant effect on the density of concrete and mortar mixtures but reduced their workability. The best values of physical and mechanical characteristics were recorded for concrete and mortar with 4% CD. The increases in the compressive strength of concrete and mortars were 6.6% and 5.7%, and in flexural strength 6.1% and 5.6%, respectively. Water absorption decreased by 9.7% for concrete and by 9.3% for mortar.