Recently, technologies involving the reuse of demolition materials from transportation structures and local industrial waste have gained increasing importance in road construction. These methods help reduce manufacturing and transportation costs while also protecting the environment. Such technologies are especially significant in regions where natural stone aggregates are scarce, particularly in the production of asphalt concrete mixes. This study investigates the possibility of producing cold asphalt concrete using metallurgical slag and recycled asphalt pavement (RAP) with foam bitumen. A comprehensive analysis was conducted of the physical and mechanical properties of slag fillers and asphalt granulate, confirming their suitability for use in road pavements. Optimal asphalt concrete formulations were developed, incorporating up to 65% RAP and 35% slag gravel, which demonstrated high compressive and tensile strength despite moderate water resistance indicators. Regression analysis was used to determine the relationships between strength characteristics and water resistance indicators and the content of components. To enhance the operational properties, a modifier based on lignosulfonates—a byproduct of hydrolysis production—was proposed. It was established that adding 5% of this modifier relative to the mineral part significantly reduces water saturation, increases the water resistance coefficient, and improves the mixture’s homogeneity. The results presented demonstrate the effectiveness of a comprehensive approach to utilizing industrial and construction waste in the production of cold asphalt concrete, ensuring ecological sustainability and economic feasibility of the proposed technology.