。
Before I could say a word, he hung up.
Literal
I [subject-が] nothing cannot-say [during-うちに] he [topic-は] phone [object-を] cut.
~ないうちに ('while not yet [verb]ing, before [verb]ing happens') is the set phrase for 'before [X] can happen.' 何も+言えない uses the negative potential — 'cannot say anything.' 電話を切る ('to hang up the phone') is the set expression. A frustrated narrative of a conversation cut short.