As the volume of polymer waste continues to grow, the development of methods for their processing and the creation of composites is an urgent task. In this work, the characteristics of sand–polymer composites based on reclaimed thermoplastics (1:3 mixture of polyolefins) are investigated. It was found that composites containing up to 75 wt% silica sand (100–300 μm) retained acceptable compressive strength (at least 25 MPa) at a strain of no more than 5%. Sand surface treatment improved the interaction between polymer and filler, increasing compressive strength by 10–15% and impact strength by 10% at 70–75 wt% of filler. The deformation and strength parameters of composites modified with carbon nanocomponents were investigated. The dependencies of compressive and bending strength on technological parameters of formation were obtained. The role of modifying components in appretization and reinforcement was shown. The introduction of technological lubricants improved homogeneity but reduced strength. The strengthening effect was related to the increase in the proportion of polymer interacting with the filler surface when the thickness of the polymer matrix reached the nanostate. The introduction of silica nanoparticles (up to 0.1 wt%) increased the compressive strength by 15%. However, the decrease in melt fluidity limited the degree of filling. The obtained composites are promising for application as structural materials in hull products used in limited climatic conditions.