Mules are notoriously stubborn (hence the word "mulish"), and to be grave is to be serious. Graves are also directly related to death, so the name suggests someone who is stubborn, seriously so, perhaps stubborn to the point of death.
Additionally, I think it is als very important that a mule is not only stubborn, but also does not have the chance to have any descendants. Just like Muley.
Graves can mean also greaves/graves, small piece of meal. He can be "eaten" very easily. Furthermore, many of similar people can be "eaten" easily. But without any meal there can not remain alive the "eater" ("the american society").
May be :)