Well to explain the process of neutralisation reactions going to completion in terms of Le Chatlier's Principle, here is the logic using examples:
Weak Acid: CH3COOH <---> CH3COO- + H+
Strong Base: NaOH ---> Na+ + OH-
So as you add more NaOH to the acetic acid solution, the H+ concentration decreases, as the OH- reacts with the H+ ions. According to Le Chatlier's principle, a chemical system at equilibrium will shift to minimise the disturbance of a change in concentration. Therefore the equilibrium for the acetic acid disassociation will shift to the RHS, in order to minimise the decrease of H+ ions. As you continue to add more and more NaOH, the equilibrium will shift to the right so much that it will become a unidirectional disassociation, hence the neutralisation reaction will go in one direction.