You use one or the other according to the gender of the thing being owned: Mit vand = my water. Min avis = My newspaper. You can check the Tips Notes for more details.
Common nouns (EN pige) se min for singuler and mine for plurals. Neuter nouns (ET vand) use mit and mite.
'mite' is not a word! For neuter gender words, the plural is also 'mine'!