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.