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

You confusion is due to the fact the most idiomatic ways to express it differs between French and English. However there are alternative forms with a closer structure in both cases.

I’ve made a mistake in my calculation.

word by word translates to:

J’ai fait une erreur dans mon calcul.

while

Je me suis trompé dans mon calcul.

literally translates to:

I mislead myself in my computation.

It’s often not a good idea to translate word for word. You made a mistake when you said “suit trompe -> have made“.

You should have included “a mistake“, but also “me“.

me suis trompé -> have made a mistake

In French, to make a mistake is se tromper. As Jlliagre said, it’s reflexive because literally it means “to mislead oneself“.

(It’s a little more subtle than that, you should go see all the meanings of “tromper” and “se tromper”.)