Nowadays, the dynamic development of the entire market of composite materials is noticeable, which is very often associated with the need to use waste or recycled materials in their production. In the process of producing composites themselves, the easy possibility of shaping their mechanical and thermomechanical properties becomes apparent, which can be a big problem for materials with a homogeneous structure. For the tests, samples made of a combination of acrylic–phenolic resin with fine aluminum and brass chips were used. The tests were performed for composite samples produced by pressing. This paper presents the results of the DMTA method of the conservative modulus and the tangent of mechanical loss angle of the composite, a detailed stereometric analysis of the surface after machining, roughness parameters and volumetric functional parameters were performed. For the tested samples, changes in the values of the conservative modulus and the mechanical loss coefficient were recorded, which indicated significant differences for the composite with brass chips in relation to composites with aluminum chips. In the case of the composite with aluminum chips, slight changes in the conservative modulus were recorded in the glass transition phase and the elastic deformation phase at different frequencies. In contrast, for composites with brass, slight changes were recorded in the entire range of the course of the conservative module as a function of temperature when different excitation frequencies were applied. In relation to the polymer matrix, a significant increase in the value of the conservative modulus of composites was recorded in the entire temperature range of the test. Significant differences were recorded in the study of the surface of composites in the case of using different materials obtained after machining as fillers. The dependences of the amplitude parameters of the surface after machining the sample made of phenolic–acrylic resin prove the poor performance properties of the surface. The use of chips in the composite significantly changed the surface geometry.