I called Susan to apologize, but get this — she just hung up on me out of the blue!

Literal

I [topic-は] Susan [to-に] apologize-volitional [quotative-と] phoned [but-のに], she [as-for-ときたら] one-sidedly phone [object-を] cut [regretful-ちゃった-んだ].

Lots going on here. 謝ろうと電話する uses the volitional+と after a verb of communication to express purpose — 'called in order to apologize.' のに is the adversative 'although, despite,' contrasting the speaker's good intentions with Susan's rude behavior. ~ときたら is a casual, often exasperated topic marker — 'as for [X], let me tell you...' 一方的に ('one-sidedly') captures the unilateral rudeness. 切っちゃった = 切ってしまった, where ~てしまった expresses completion with regret or annoyance. The final んだ adds explanatory emphasis.