Mother woke me up saying, 'It's 7:15.'

Literal

Mother [topic-は] '7:15 is-よ' [quotative-と] saying I [obj-を] woke.

A direct quotation wrapped in 「」 brackets and anchored by the quotative particle と. 言って is the te-form of 言う, chaining into the main verb 起こした. The sentence-final よ inside the quote is assertion particle ('I'm telling you,' 'for your information'), adding a nudging tone that fits a parent waking a child. The matrix structure is '[quote] と言って Xを起こす' — a common frame for reporting what someone said as they did something.