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I think it's an example of alliteration and onomatopoeia; the adjacent "pop" and "cap", both of which imply action, can both mean to finish or to kill off. So it generally means to "whack" or "take out". "I oughta pop a cap in your [...] [...] ass". "Your ass" is a synonym for "you", and "ass" often gets prefixed with another contextual epithet, e.g. "dumb", "white", "nigger", "theivin'", "junkie"; and with other, more expansive terms.
Great that you brought in the sounds. It's actually consonance with pop cap and assonance with all the short 'a's gonna a cap ass (alliteration 'a' and 'ass') I think you could argue the sentence is also onomatopoeia for beating someone. In your version I'm gonna pop a cap in your ass. has that nice iambic with a finishing anapest melodrama.
Couple of things: "In your ass", is that you are raped - and that it means nothing to me. Rather like "fuck you" or "I'll rape your helpless ass, you piece of shit". "pop a cap", to equate trying to murder you as of no more significance that opening a bottle of soda for a drink. basically, a feigned immense superiority perhaps to support potentially forthcoming retarded bravado. please, don't drink my milkshake.