'My' is not a possessive pronoun and 'Mine' is a possessive pronoun.

'My' is a determiner which is always used before a noun.

For Example: My Book. Not, Mine book.

Once you have mentioned the Noun, you can use the pronoun i.e., the possessive pronoun 'Mine'

Example: A: Can you give your book?
B: Nope.
C: Please, take mine. (Since there was a noun (Book) already mentioned, a pronoun can be used.