Yes, "mine" is a possessive pronoun, and la mienne is its feminine singular equivalent. French possessive pronouns always begin with an article - see Le mien/le tien/le sien/etc = Mine/yours/his/hers/its (French Possessive Pronouns)
I understand, so because it is followed by an article "la mienne" c'est is used.
Can I say "Cette robe que je porte au travail" instead of,
"C'est la robe que je porte au travail"
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