Far from being pleased, she's furious about it.

Literal

She [topic-は] that matter [for-で] is-pleased far-from, very is-angry.

~どころか ('far from / let alone') is the contrastive intensifier par excellence: it sets up an expectation only to overturn it with something stronger. Here 喜んでいるどころか ('far from being pleased') primes the reader for surprise, and とても怒っている ('very angry') delivers the contrast. The で here is causal — 'because of that matter'. ~ている here marks ongoing emotional state (anger persisting through time), not a one-shot event of getting angry.