We explore the intramolecular spin interactions of the core-modified porphyrin diradicals with a CC unit (R-(CC) and R-(CC)2+) featuring (CC)porphyrin and (CC)porphyrin2+as the couplers and verdazyl, nitronyl nitroxide, and imino nitroxide as spin sources (R) at the B3LYP/6-31G(d) level and the CC effect through comparison with the porphine-coupled diradicals (R-(Null)). Structurally, modifications of porphine through introducing radical groups to the edge sites and a CC unit to its core lead to a nonplanar diradical structure featuring a curved (CC)porphyrin coupler and twist linkages of radical groups. Although such nonplanar structures seem unfavorable to the spin coupling between spin sources, our results suggest that the core modification with a CC unit noticeably enhances the spin couplings in R-(CC) and R-(CC)2+compared with R-(Null) with a planar porphine coupler, and R-(CC) possess mild ferromagnetic couplings but R-(CC)2+present strong antiferromagnetic ones, indicating that two-electron redox can switch the magnetisms. The differences in the magnetic properties and coupling magnitudes should be attributed to distinctly different spin-interacting pathways among R-(Null), R-(CC), and R-(CC)2+. Besides, the energies of the lowest unoccupied molecular orbitals of the couplers regulate the magnetic couplings, and the linking modes of the radical groups to the couplers also affect the magnetic coupling strengths especially for R-(CC)2+. The observed magnetic coupling regularities are reasonably analyzed by the modified spin alternation rule. This work provides a promising strategy for rational designs of the porphyrin-based diradicaloids and new insights into the spin interaction mechanisms in such diradicaloids which are useful bases for further applications in the future.