Change the sentence into indirect speech.
She said, "The bag is mine." 

The correct statement is "She said that that bag was hers." In indirect speech, the pronoun 'this' becomes 'that' and the pronoun 'mine' becomes 'hers'.
The present simple tense format 'subject + V1 (is) + object' will be changed into the past simple tense format 'subject + V2 (was) + object'.