。
She blamed him for being late.
Literal
She [topic-は] he [subject-が] was-late [saying that-といって] blamed.
~といって is the te-form of 言う ('say') with the quotative と, used to attribute spoken or implicit grounds for a subsequent action — 'saying that ~' or 'on the grounds that ~.' With 責める ('blame, scold'), it specifies what she blamed him for.