Polymer mechanochemistry induces chemical reactivity by applying a directed force, which can lead to unexpected reaction mechanisms. Strained cyclic molecules are often used in force-sensitive motifs because of the strong force coupling of ring-opening reactions. In this computational study, the force dependence of the ring-opening reactions of oxirane will be investigated. Density functional theory and multireference methods were used to investigate the electronic character of both symmetry-allowed and symmetry-forbidden reactions. In the latter case, an orbital crossing occurs during the reaction course, forcing the Woodward-Hoffmann-forbidden reaction to proceed via a diradical pathway. The performance of broken-symmetry density functional theory is evaluated and compares well to high-accuracy CASPT2, MRCI, and ic-MRCC computations. Due to the high ring strain, the barrier heights of both ring-opening reactions are steeply reduced by the application of an external force. Furthermore, the use of unsaturated linkers was shown to yield a significant reduction of the barrier heights, explaining previous experimental findings. Finally, we show through analysis of the PES topology how the external force transforms characteristic points such as saddle points and bifurcations, providing insights into force-dependent mechanism changes.