、。
She made me so furious on the phone that I hung up on her.
Literal
She [topic-は] phone [by-で] me [object-を] very much enraged-made [because-ので], I [topic-は] her [with-との] phone [object-を] hung-up.
Two causative constructions make this sentence dense: 立腹させた (made [me] furious, using the formal 立腹 'indignation') and the resulting action. 立腹 is a Sino-Japanese compound that's more bookish than 怒る. The ~ので links cause to consequence. 彼女との電話をきった specifies 'the phone call with her' as what was cut.