Mechanical forces can induce chemical reactions, produce chemical signals, and alter reaction kinetics. Here, using magnetic tweezers-based single-molecule force spectroscopy, we study the force effects on the ring-opening metathesis polymerization (ROMP) of single-polymer chains, during which nonequilibrium conformational entanglements can form and unravel stochastically. We find a surprising, biphasic force dependence of polymerization kinetics: The single-chain polymerization rate initially slows down with increasing stretching forces, reaching a minimum, and then accelerates at higher forces. Analysis of real-time single-chain growth trajectories allows for dissecting the polymerization process into two distinct regimes, one with and the other without entanglement formation, unveiling the biphasic force dependence in both regimes. Two different mechanisms likely operate for the biphasic dependence: a force-induced entanglement tightening and then splitting and a force-induced catalyst structural distortion that switches the reaction pathway between reactant states of different stability and reactivity. These findings and insights point to opportunities of using force to manipulate polymerization reactions and tune the physiochemical properties of synthetic polymers.