"The bag is mine."
Translation:La borsa è la mia.
The meaning would be pretty close, but at this point there are certain grammar concepts we're trying to reinforce. Think of it like this: it is my bag and the bag is mine are slightly different, you wouldn't be able to say it is mine bag or the bag is my. In è la mia borsa and la borsa è la mia the pronoun and the adjective look the same, but they are two different parts of speech. È la mia borsa = adjective, La borsa è la mia = pronoun.