To develop novel mineral-filled composites and assess their enhanced properties (stiffness, a good balance between mechanical strength and impact resistance, greater temperature stability), a high-impact polypropylene copolymer (PPc) matrix containing an elastomeric discrete phase was melt mixed with natural CaSO4 β-anhydrite II (AII) produced from gypsum rocks. First, in a prior investigation, the PPc composites filled with AII (without any modification) displayed enhanced stiffness, which is correlated with the relative content of the filler. The tensile and impact strengths dramatically decreased, especially at high filling (40 wt.%). Therefore, two key methods were considered to tune up their properties: (a) the ionomeric modification of PPc composites by reactive extrusion (REx) with zinc diacrylate (ZA), and (b) the melt mixing of PPc with AII surface modified with ethylenebis(stearamide) (EBS), which is a multifunctional processing/dispersant additive. The properties of composites produced with twin-screw extruders (TSEs) were deeply assessed in terms of morphology, mechanical, and thermal performance, including characterizations under dynamic mechanical solicitations at low and high temperatures. Two categories of products with distinct properties are obtained. The ionomeric modification by Rex (evaluated by FTIR) led to composites characterized by remarkable thermal stability, a higher temperature of crystallization, stronger interfacial interactions, and therefore noticeable mechanical properties (high tensile strength (i.e., 28 MPa), increased stiffness, moderate (3.3 kJ/m2) to good (5.0 kJ/m2) impact resistance) as well as advanced heat deflection temperature (HDT). On the other hand, the surface modification of AII with EBS facilitated the dispersion and debonding of microparticles, leading to composites revealing improved ductility (strain at break from 50% to 260%) and enhanced impact properties (4.3–5.3 kJ/m2), even at high filling. Characterized by notable mechanical and thermal performances, high whiteness, and a good processing ability, these new PPc–AII composites may be tailored to meet the requirements of end-use applications, ranging from packaging to automotive components.