While waste plastics have been used as a natural sand aggregate replacement in cementitious mortar as a sustainable option to mitigate global accumulation of plastic waste in landfills, fundamental mechanical properties like compressive, tensile, and shear must be known to advance design and practical application of these cement-concrete composites as suitable building construction materials. Experimental testing is conducted to reveal to what extent the cementitious composite properties are altered, thereby influencing their overall mechanical performance, when both ungraded and graded ground recycled acrylonitrile butadiene styrene (GRABS) plastic are employed as substitutes for natural aggregates. The novelty of this research lies in its pioneering investigation to quantify the effects of varying particle sizes and volume fractions of waste plastics acquired through mechanical recycling and their influences on the mechanical properties of mortars containing plastics as a composite material. The results from fresh and hardened material properties are compared to conventional mortar properties to examine the impact of various GRABS particle sizes and volume fractions on the overall material strength. While replacing sand with waste plastic generally reduced mechanical properties, the resulting mixes still met the minimum compressive strength (4060 psi [28 MPa]) as per ASTM C150 standards for Portland cement. Notably, graded plastic particles with sizes less than 0.024 in [0.6 mm] demonstrated an overall improvement in mechanical properties compared to ungraded particles. Failure mechanisms responsible for compressive, tensile, and shear damage development are discussed by analyzing the fracture surfaces, which provide insight into the intricate relationship between waste plastic size and distribution on the mechanical behavior of mortar. The findings indicate that GRABS waste plastics, when combined with sand at appropriate particle sizes and volume fractions, have the potential to create tailored mixes to meet minimum mix design standards for construction applications.