。
She hung up without saying goodbye.
Literal
She [topic-は] goodbye [also-も] not-saying-and phone [object-を] cut.
電話を切る ('to cut the phone' = 'to hang up') is the standard collocation for ending a call, dating from the era when one literally cut the line. ~ずに is the classical/literary 'without doing,' a slightly more formal cousin of ~ないで. The も on さよなら adds 'even' — 'without even a goodbye.' Hanging up mid-conversation, especially without a closing, is recognizable as a sign of frustration, distress, or anger across cultures, but in Japan the social cost is even sharper: phone etiquette dictates a clear closing exchange (失礼します or similar), and the absence of one is a deliberate signal.