How can I delete a person in my tree added by someone else ?

@Valbuena, Profiles are not generally "Deleted" but relationships can be removed.

Remember, you do not have a private personal tree (other than your living profiles). FamilySearch's Family Tree is one community/shared tree.

Some other user thought and had reasons to believe that this person should be connected. You first have to be sure that this person is not properly connected to the FamilySearch tree. If so you can simply remove the relationship by clicking on the pencil icon in the Family Members section of the person Detail page and responding to the prompts.

Some more detail about why you feel this person does not belong and posting the PersonID will be helpful for others to respond more specifically.