。
She was so angry she couldn't even speak.
Literal
She [topic-は] anger [possessive-の] excess [from-あまり] mouth even could-not-use.
~のあまり marks an excess of emotion that causes a consequence — 'so much X that Y.' Here, 怒りのあまり → 口も利けなかった: the anger was so intense she couldn't even use her mouth (speak). 口を利く ('to speak / use one's mouth') is a set expression, and 利けなかった is its potential negative past. The particle も ('even') emphasizes the extremity.