The reaction mechanisms of two inhibitors TFK+ and TFK0 binding to both the wild-type and H447I mutant mouse acetylcholinesterase (mAChE) have been investigated by using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) approach and classical molecular dynamics (MD) simulations. In the wild-type mAChE, the binding reactions of TFK+ and TFK0 are both spontaneous processes, which proceed through the nucleophilic addition of the Ser203-O-gamma to the carbonyl-C of TFK+ or TFK0, accompanied with a simultaneous proton transfer from Ser203 to His447. No barrier is found along the reaction paths, consistent with the experimental reaction rates approaching the diffusion-controlled limit. By contrast, TFK+ binding to the H447I mutant may proceed with a different reaction mechanism. A water molecule takes over the role of His447 and participates in the bond breaking and forming as a "charge relayer". Unlike in the wild-type mAChE case, Glu334, a conserved residue from the catalytic triad, acts as a catalytic base in the reaction. The calculated energy barrier for this reaction is about 8 kcal/mol. These predictions await experimental verification. In the case of the neutral ligand TFK0, however, multiple MD simulations on the TFK0/H447I complex reveal that none of the water molecules can be retained in the active site as a "catalytic" water. Furthermore, our alchemical free energy calculation also suggests that the binding of TFK0 to H447I is much weaker than that of TFK+. Taken together, our computational studies confirm that TFK0 is almost inactive in the H447I mutant and also provide detailed mechanistic insights into the experimental observations.