Where does "my ass" come from?

Solution 1:

I watch a lot of westerns about cowboys in the old west (US). It seems to me that there are many references to saving hides (of cattle, also heads of cattle, another way to refer to the number of animals) and conjecture that it's possible that the expression "save my ass" started out as "save my hide". This is the NGram chart that shows the usage overlap:

According to this chart, "save my ass" started to gain in popularity when usage of "save my hide" began to wane.

Solution 2:

The phrase my ass meaning me as a person seems to be closely akin to your ass when addressed to that person.

These phrases seem to be well established by the early 1950s when both Salinger (freezing my ass off [Catcher in the Rye]) and Jones (What if they threw my ass in jail? [from Here to Eternity]) used them in novels.

Your ass referring to the whole person dates back to at least 1936 in Farrell's A world I Never Made (shagging your ass down from the tops of buildings)

There are numerous early 20th century uses of the term ass referring to infliction of injury, many of which sound like attacks that would not be limited to the buttocks. It may be that, as kicking one's ass came to refer to a triumph over the entire being, the use of ass to refer to that being slid into common usage.

As an aside, the use of a part to refer to the whole is an example of synecdoche.

Solution 3:

The concept of referring to whole people by various body parts is nothing new in the English language.

For example:

Deck hands.
Counting heads.
Another pair of eyes.
Every swinging dick in this company . . . (See the movie Heartbreak Ridge to hear this many, many times.)

Self-reference to one's ass or someone else's ass is just an extension of this principle.

It seems likely that the first usage of ass in this sense was Get my ass to ... Literally, to transport one's ass (and presumably the rest of them) to another location. There are other variants of this as well: Get your butt in gear. Get your feet moving. etc.

As to it's prevalence here is an NGRAM including many of the variants and common phrasings click to enlarge, there is a clear spike of both uses from the 1940s, and, including them in phrases like get your ass spiked in the 1960s. So, it seems like the usage began to go up around the major wars fought by the United States in that time period. (The Korean War and Vietnam War.)

Click to Enlarge: