The pursuit of sustainability in the construction and demolition (C&D) sector calls for effective decision-making strategies, both in terms of technical and environmental sustainability, capable of mitigating its huge demand for resources and emissions to the environment. The recycling of C&D waste is one of the potential solutions that could reduce the extraction of virgin materials as well as waste generation and landfilling. This study evaluates and compares, by means of the Life Cycle Assessment (LCA) approach, the production of concrete via five different mixtures made up of coarse natural aggregates (NA, primary, virgin materials), and coarse recycled concrete aggregates (RCA, recovered from previous uses). The present study assesses the environmental load of concrete production, by means of mixtures containing only coarse NA and mixtures with coarse RCA produced in fixed and mobile treatment plants, to be replaced with 30% and 100% of coarse NA by weight. The results point out that the use of coarse RCA in concrete mixtures provide greater energy savings and environmental advantages compared to the concrete with only coarse NA; the improvement increases up to a 100% replacement rate by weight of coarse NA with coarse RCA in the mixtures. In this case, the reduction of the impacts is significant for some impact categories such as freshwater ecotoxicity (−63.4%), marine ecotoxicity (−76.8%), human carcinogenic toxicity (−27.1%), human non-carcinogenic toxicity (−77.9%), land use (11.6%), and water consumption (−17.3%), while the total CED impacts decreases by about 10% and that of GWP by 0.4%. Results are discussed in light of the urgent need for advancing circular economy concepts and practices in the C&D sector and decrease the large use of primary resources (in particular sand and gravel). The replacement of NA with RA by weight could contribute to reducing the impacts of the C&DW management and disposal. For this to happen, further improvement of the quality of recycled aggregates is essential for their market development as well as dedicated policies and legislations.