Hazrat Abu Hurairah radiyallahu anha says that he once saw Rasoolullah sallallahu alaihe wasallam eat a piece of cheese then perform wudhu. Then he saw him at another time eat a shoulder of a goat, and perform salaah without performing wudhu.
In the early stages of Islam, wudhu would become nullified after taking food and drink cooked on fire. Later this law was abrogated. It is possible that Sayyidina Rasoolullah sallallahu alaihe wasallam performed wudhu after eating cheese in the days when wudhu became nullified after eating things that were cooked on fire, or he may have performed wudhu due to some other reason. For example, he may have performed wudhu again whilst still being in the state of wudhu, or due to some reason the wudhu may have become invalid. From the explanation given by Sayyidina Abu Hurairah radiyallahu anhu we gather that in the early stages of Islam, Sayyidina Rasoolullah sallallahu alaihe wasallam performed wudhu after eating things cooked on fire. Later this law was abrogated, that is why he did not perform wudhu after eating the mutton.