Originally just the name for the donkey, this word had no filthy connotations until about the late 1700s, early 1800s, when the
pronunciation of true (English) word for the backside, "arse", had changed enough to sound much like "ass", seeing as how the English often don't pronounce the "r" when they speak.
To avoid any unwanted baggage associated with the word, the name of the ass was changed to "donkey". As a result, the word "arse" has disappeared from American
vocabulary.
Although before
World War I they were similar, the British pronunciations of "ass" /æs/ and "arse" /ɑːs/ are now very different.