The "yet" and the "of" aren't tied together. We could modify the sentence like this: This austerities biggest casualty yet is the shelving of a $5.92 billion .... P.S.: "resource" and "casualty" in your sentence are both misspelt.

As others have said, the pair of "yet of" is not an expression. The word "yet" is an adverb of time that means the same thing as "so far" or "from the beginning until now". The word "of" is a preposition that introduces a very long prepositional phrase, "of the mining giant's austerity effort prompted by slumping iron-ore prices and billion-dollar write-downs". The prepositional phrases functions as an adjective that describes the noun "the biggest casualty".

Thank you! Now I'm clear how to use "yet" (^^)v.

Using other words you can replace that section of text with: "... the biggest casualty so far, from the mining giants austerity effort ..."