Mother [topic-は] me [to-に] stay-up-late do-[negative-imperative-な] [quotative-と] always is-saying-[polite-ます]
するな is the plain negative imperative: 'don't do!' — blunt and direct. 夜更かし (よふかし) = staying up late. と marks the quoted command. いつも言っています = 'always says' (ongoing habitual).