。
She spoke through her tears.
Literal
She [topic-は] tears mixed-in [manner-に] spoke.
涙まじりに (なみだまじりに) means 'with tears mixed in, tearfully' — まじり is the noun form of 混じる ('to be mixed'). The に makes it an adverbial expression describing the manner of speaking. A compact and natural way to describe tearful speech.