They're both possessive - but "my" is an adjective which is used to describe nouns, while "mine" is a pronoun.
So you get "it is my sandwich" because "my" describes that the sandwich belongs to you. But you can't say "it is my", because you need a noun with it.
You also get "it is mine", but you can't say "it is mine sandwich", because the "mine" describes "it" and not a noun that follows. Hence, "the sandwich is mine" really means "the sandwich belongs to me", while "it is my sandwich" means "it is the sandwich which belongs to me".
So do 'min' and 'mitt' both translate as 'my/mine'? Is that the same for 'mina' too? 'Smörgåsarna är mina'?