Is the word mine a personal pronoun?

No, the pronoun 'mine' is a possessive pronoun.

A possessive pronoun is a Word that takes the place of a noun that belongs to someone or something.

• The possessive pronoun 'mine' is a first person, singular pronoun.

A personal pronoun is a Word that takes the place of a noun for a specific person or thing.

• The corresponding first person, singular, personal pronouns are 'I' and 'me'.

Example uses:

I bought a new car. (the personal pronoun 'I' is the subject of the sentence)

That red car is mine. (the possessive pronoun 'mine' takes the place of noun 'car')

Take a ride with me. (the personal pronoun 'me' is the object of the preposition 'with')

Note: The corresponding first person, singular, possessive adjective is 'my', a Word placed before a noun to describe that noun as belonging to the speaker.

Example: My car gets good gas mileage.