Millions of people worldwide suffer from musculoskeletal damage, thus using the largest proportion of rehabilitation services. The limited self-regenerative capacity of bone and cartilage tissues necessitates the development of functional biomaterials. Magnetoactive materials are a promising solution due to clinical safety and deep tissue penetration of magnetic fields (MFs) without attenuation and tissue heating. Herein, electrospun microfibrous scaffolds were developed based on piezoelectric poly(3-hydroxybutyrate) (PHB) and composite magnetic nanofillers [magnetite with graphene oxide (GO) or reduced GO]. The scaffolds' morphology, structure, mechanical properties, surface potential, and piezoelectric response were systematically investigated. Furthermore, a complex mechanism of enzymatic biodegradation of these scaffolds is proposed that involves (i) a release of polymer crystallites, (ii) crystallization of the amorphous phase, and (iii) dissolution of the amorphous phase. Incorporation of Fe3O4, Fe3O4-GO, or Fe3O4-rGO accelerated the biodegradation of PHB scaffolds owing to pores on the surface of composite fibers and the enlarged content of polymer amorphous phase in the composite scaffolds. Six-month biodegradation caused a reduction in surface potential (1.5-fold) and in a vertical piezoresponse (3.5-fold) of the Fe3O4-GO scaffold because of a decrease in the PHB β-phase content. In vitro assays in the absence of an MF showed a significantly more pronounced mesenchymal stem cell proliferation on composite magnetic scaffolds compared to the neat scaffold, whereas in an MF (68 mT, 0.67 Hz), cell proliferation was not statistically significantly different when all the studied scaffolds were compared. The PHB/Fe3O4-GO scaffold was implanted into femur bone defects in rats, resulting in successful bone repair after nonperiodic magnetic stimulation (200 mT, 0.04 Hz) owing to a synergetic influence of increased surface roughness, the presence of hydrophilic groups near the surface, and magnetoelectric and magnetomechanical effects of the material.