What is the ruling of Islamic law regarding how to deal with a father who abuses his daughter and prevents her from marrying a committed man on the pretext of completing her studies, especially given that there is a relationship "that has crossed boundaries" between the daughter and the aforementioned person?

You must cut off the relationship with this young man and adhere to the boundaries of Allah, for your father's refusal of marriage is not a justification for the continuation of the relationship. Strive to convince your father to expedite the marriage, and mediate through some wise individuals to speak with him, clarifying to him that he is not permitted to prevent your marriage to a suitable man without a valid reason; otherwise, you both must be patient and chaste until the marriage becomes facilitated.