"She is abused, stol'n from me, and corrupted" - Brabantio (man sitting) is frustrated by Othello's relation with his daughter, Desdemona. He believes that Othello is corrupt and has abused her to establish a relationship.
"By spells and medicines bought of mountebanks" - Brabantio has convinced himself that the only way that Othello could have possibly formed a relationship with Desdemona is through witchery.
"Sans witchcraft could not." - Brabantio is stating that only through witchcraft this relationship was able to form, without witchcraft they would not be together.