How can I deal with a professor with an all-or-nothing grading habit?

This may be almost too obvious to be worth mentioning, but one idea you could consider is to study really really hard for this class in order to make sure you do not end up in the group of people who fail it, large though that group may be. It sounds like it’s not impossible to do well in the class, just more difficult than you are used to. A relevant idea to keep in mind is that you have control over the outcome: the belief that you can adapt your behavior to the situation and achieve a successful outcome is what is known as a growth mindset. It’s a powerful idea and very worth thinking about, both in the current context and for anything else you aim to do in the future.

That being said, it’s possible that the professor is unreasonably harsh in his grading methodology. Failing that many students by setting standards that are so high as to be nearly unattainable does not benefit either the students or the university (or future employers of those students), and results in a waste of resources and a drain on the students’ morale. Certainly preventing students from taking the final exam because of poor performance in the midterm is a rather extreme step, and contradicts much of what I know about best practices in education.

So, at the same time that you are working hard to succeed in the class, it’s completely reasonable to try to get the university to see that there is a problem and put pressure on the professor to change these policies. Some avenues that you can explore are to bring the matter up with the dean, the university ombuds person, your student union, or other types of student advocates that may be available. A local student or town newspaper or news website may also take an interest if this is an issue that affects a large number of students. If you are savvy with social media, you could drum up interest through Facebook or other social media, and attract support for your cause.

Good luck!

Edit: based on the discussion in the comments, many people seem to think my social media idea is a really bad one. I don’t completely understand their objection (the main reasoning given is the idea that social media are a “cesspit”, so it may simply reflect a dislike of social media in general and a belief that you shouldn’t use it for any purpose), but it’s possible they have a point, so keep that in mind. In any case, my suggestion is not meant to be understood as an endorsement of social media in general, only as a suggestion that social media may be useful as an advocacy/campaigning tool in a specific situation like yours.

The honest answer to your question "how to deal with..." is to work hard and study so you will score the required minimum 30/100 on the midterm. And then continue working hard so you learn the material well enough that you can correctly answer many questions on the final. Good luck!

I think that if the university permits this sort of thing that you have little recourse.

You could complain to their superiors, of course. Perhaps you could drop the course.

If I were the department head over this person, or a dean, I'd want to have a talk with them to see how they might justify this. I think, personally, that it would be hard to justify, but it might be possible, depending on the subject matter and field. If you are studying math, for example, I don't see much possibility of a justification. But if your knowledge and behavior in your field might put other people at serious risk in some way, then there might be some argument for a very severe filter.