In view of the unique structures and promising applications of porphyrins and their derivatives, exploration of their various properties has continued to a hot topic. In this work, we combine porphyrin-mimetic graphene patches which are core-modified by a CC or a B–B unit and two nitroxide radical groups to construct a series of novel diradical molecules (the CC-cored or BB-cored molecules). The spin coupling constants (J) of diradicals were calculated at the (U)B3LYP/6-311G(d,p) level by considering the different linking modes of two nitroxide groups. The results indicate that different core modification considerably affects the J values of such diradicals, and the linking modes can tune the sizes and signs of J, changing their magnetic coupling interactions with different magnitudes and the signs of J from antiferromagnetic to ferromagnetic or vice versa. More interestingly and importantly, the spin coupling interactions of the CC-cored molecules can also be tuned by stretching the core unit C–C bond, suggesting the possibility of activating specific vibrational modes of the CC-cored diradicals by energy pulses to yield variable J coupling magnitudes. On the other hand, for the BB-cored molecules, two-electron reduction can switch or tune their magnetism from ferromagnetic to antiferromagnetic. The essence of all observations is further analyzed from the structural effects and orbital and spin density distributions. The findings about magnetic regulation in these core-modified porphyrin-mimetic graphene patch nitroxide diradicals further expand the field of molecular magnets and provide a rational theoretical basis for designing novel building blocks of magnetic functional molecular materials.