This event in the book occurs in Chapter Six, which is where Matt Boner's mule is first introduced to us, and his pitiful life is described before he dies. When he does pass on, the mule is dragged out to the outskirts of the town for sanitary reasons and they have a mock "funeral" for the mule. Note how the animals who attend this funeral are described:
[The buzzards] were holding a great flying-meet way up over the heads of the mourners and some of the nearby trees were already peopled with the stoop-shouldered forms.
The mule, who was prized as being so important to the community, is left to be scavenged by the buzzards. The mule is a very important symbol in the book, as remember Janie's grandmother describes black women as being "de mule uh de world." If we examine Matt Boner's mule therefore we can see it as a symbol of Janie and how she feels harrassed and mistreated by men, and her death surely signals the death of her spirit within her thanks to the way she is protected and claustraphobically looked after in her present relationship.
In Their Eyes were watching God it is the buzzards that attend the mule's funeral by the swamp. The buzzards even take on human voices and refer to the mule as if it was a 'man.'
The mule's funeral and any attendance there is significant due to the fact that Nanny says early in the story that
nigger woman is de mule uh de world
signifying that the mule represents much more in the story than just a mule that Jody effectively 'rescues' to allow it to rest in peace before its death. The mule somehow represents Janie's own plight and helplessness. It
cannot fight back due to the constant pressure to which he has been subjected.
Joe is recognised as the one saving the mule, although he only does it because he sees Janie's distress.
Refer to the eNotes pages and navigate to the summaries and even the previously asked questions to understand the significance of instances in the novel such as the mule's funeral.