The sergeant does this because when he first tells the Whites that the monkey's paw has the power to grant a person three wishes, they simply do not take him seriously. Mrs White remarks that the story sounds like something out of the Arabian Nights, which are well known as tales of pure magic and fantasy.
Mrs White goes on in the same frivolous manner:
Don't you think you might wish for four pairs of hands for me?
Then the Whites all laugh as the sergeant hastily intervenes to prevent Mr White from making such a ridiculous wish.
The sergeant actually believes in the paw's abilities because, as it seems, he has experienced them for himself with grim results, while the Whites are just treating it all as a huge joke at this stage. However, they are very soon to have a wish granted in the most appalling manner, and then the mood changes and remains dark for the rest of the story. In fact, the tale becomes one of gothic horror, although the horror remains powerfully understated.