This particular verb in French that means "to make an error", "to err", is a pronominal verb; it's just like that; you can use other verbs, but they are not heard so often and they are verbal locutions instead of simple one word terms: "commettre une erreur", "faire une erreur". In a pronominal verb, just as in English, you have to use the pronoun all the time; there is no way to omit it. This pronoun, moreover, has nothing to do with the possessive adjective "mon"; that word is in the noun group not the verb group: you can replace it by all of these words in turn and say something a little different each time without changing the verb;
ce, le, un, leur, ses, mes, tous ces, certains, etc. ("calcul" or "calculs" according to gender)
The conjugation is as follows ;
je me suis trompé
tu t'es trompé
il s'est trompé
nous nous sommes trompés
vous vous êtes trompés
ils se sont trompés