As a student planning a Mut'a marriage, I am facing difficulties because the girl's father has denied permission by placing a very high Mahr and also wants her to finish her education first. In this context, is it allowed to proceed without his consent?
Bismihi ta'āla
Education is not an obstacle for marriage, and will not hinder a person in finishing their degree. However, why would you plan to do mut'ah. Why don't you marry her, and maybe postpone the wedding and moving in until both of you are ready. At least you will be halal to each other.
To answer your question, no, it is not allowed to proceed without his consent. Neither of you should even think about taking things into your own hands and doing things outside the conventional way of how people marry.
Consider all other options, and consult with respectful elders and scholars before you take any steps in this.
And Allah knows best