Is something being omitted here? Is it just a figure of speech?
Nothing is omitted there.
This 「が」 is a sentence-ending particle expressing an insult, swearing, cussing, etc.
It is very often pronounced 「がっ」 by us native speakers.
"You little slip of a girl!" or
"You little bi***!"
The "right" translation will always depend on the context.
The suffix of insult 「め」 is often inserted between the noun and the 「が（っ）」 (but not in that clip).
I spoke to my professor, and he said the other answer is "extremely wrong"
が is not an SFP [(Sentence Final Particle)], and there's nothing inherently insulting about it. It's just a plain-old nominative marker. As you know, the new information comes before the が. Hence, the entire rest of the sentence is omitted as old (or inferrable) info.
A potential predicate there could be 何を言っているのだ