。
She got angry at what I said.
Literal
She [topic-は] I [subject-が] said thing [reason-で] stomach [subject-が] stood.
The で here marks the cause or reason — 'because of / over what I said.' 言ったこと ('the thing I said,' literally 'what was said') is the headless relative-style nominalization that names the trigger. 腹を立てる ('to get angry,' literally 'the belly stands up') is the body-part idiom for anger — Japanese locates strong emotion in the abdomen rather than the heart. The cause-marking で is one of に's main competitors — both can mark reason in different patterns; で typically marks causal events ('over X / because of X') while に tends toward reactions to stimuli.