。
She raised her child at the cost of her own life.
Literal
She [topic-は] her own life [object-を] sacrifice-do [then-て] child [object-を] raised.
~を犠牲にして is the て-form of 犠牲にする ('to sacrifice [X], give up [X]'), here connecting 'sacrificing one's life' as the means or precondition for 'raising the child.' 生活 ('life, livelihood, daily life') is broader than just 'life' in the abstract sense — it encompasses how one spends one's days, including comforts, free time, career. So she gave up not survival but her own daily existence — leisure, freedom, perhaps career — in order to raise her child. 育てる ('to raise, bring up') is the standard verb for child-rearing.