Among spin-crossover complexes, Fe-porphyrin (FeP) stands out for molecular spintronic applications: An intricate, yet favourable balance between ligand fields, charge transfer, and the Coulomb interaction makes FeP highly manipulable, while its planar structure facilitates device integration. Here, we theoretically design a mechanical spin-switch device in which external strain triggers the intrinsic magneto-structural coupling of FeP through a purely organic embedding. Exploiting the chemical compatibility and stretchability of graphene nanoribbon electrodes, we overcome common reliability and reproducibility issues of conventional inorganic setups. The competition between the Coulomb interaction and distortion-induced changes in ligand fields requires methodologies beyond the state-of-the-art: Combining density functional theory with many-body techniques, we demonstrate experimentally feasible tensile strain to trigger a low-spin ($S=1$) to high-spin ($S=2$) crossover. Concomitantly, the current through the device toggles by over an order of magnitude, adding a fully planar mechanical current-switch unit to the panoply of molecular spintronics.