With increasing limitation of petrochemical resources, there is a growing demand for the replacement of nonrenewable fiber-reinforced polymer composites by renewable polymer composites. Therefore, the aim of this research work was to improve the mechanical properties of bast (plant) fibers reinforced polymer composites without reducing their renewable material content. To achieve this goal, basalt fibers (natural mineral fibers) were used to partially substitute the amount of bast fibers in the polymer composites. The applied fibers were processed to semi-finished materials by carding and needle punching and processed further by afterwards press-molding. An intense optimization of the carding process led to the production of homogeneous fabrics based on various types of fibers (bast, basalt and PP). The homogeneity of the fabrics was confirmed by scanning electron microscopy (SEM) analysis of the composites. Several composites based on polypropylene and acrylate thermoset resin, reinforced with merely bast fibers, were prepared as reference. In the next steps, the bast fiber content of the reference compositions was partially replaced by basalt fibers. The compression-molded samples were tested for their flexural, tensile, and impact energy properties. The very positive finding was that the addition of basalt fibers not just improved significantly the strength and stiffness of the composites, but simultaneously increased the properties of the composites regarding energy absorption, a key requirement in the automotive industry. The fracture surface analysis confirmed a better fiber matrix adhesion in thermoset composites compared to thermoplastic composites. The tested renewable hybrid polymer composites have great potential to replace nonrenewable fiber-reinforced polymer composites.