How to deal with students leaving the class for 10 min during the lecture?
The existing answers seem to me extreme. I don't think some sort of draconian blanket "leaving-the-room policy" is needed here. I would suggest the following:
For students leaving occasionally: Ignore it. They are adults and sometimes things in their lives may take higher priority than your class (e.g. going to the bathroom, feeling unwell, family emergencies, etc). If it's distracting to you, well, deal with it. It's a classroom, not a funeral, and you are a professional. Take a breath and get back to teaching.
If you see a particular student leaving often: Have a private word with them to see if things are okay. They may have special circumstances that you don't know about (chronic illness is one distinct possibility). Once you know their situation, you may be able to offer specific suggestions that will reduce the disruption and/or get them more engaged in the class.
If, after talking to them, you are convinced they are just walking out from spite, and they won't stop: Follow your institution's policy on disruptive students. Your department chair should have further guidance. It may ultimately be necessary to drop them from the class.
A short break in the middle of a 75-minute class is a reasonable idea, but I would keep it very short: perhaps 1-2 minutes, enough to stand up and stretch, not more. It should not significantly reduce the amount of time students spend on task. (Otherwise, as mentioned above, you may encounter problems with your institution's authorities that your class does not provide as much instructional time as promised by its number of credit hours. Moreover, some students will see it as wasted time and resent it.) Better yet, break up the lecture with some other sort of productive activity (small group discussions, problem solving, etc).
I don't think it's appropriate to publicly shame students for poor etiquette, or shut them out of class if they leave. You will unfairly punish students who legitimately need to step out for a few minutes, and anyone who is doing it from spite or boredom will just be further alienated.
Have a 10-minute break in the middle of the lecture. (E.g., 35min lecture + 10min break + 30min lecture = 1h 15min in total.)
1h 15min is far too much without any breaks. There are plenty of studies that show that students do not really pay attention to the lectures more than for maybe 20-30 minutes in the beginning of the lecture (and for a short period of time right before the lecture ends), so by telling everyone to take a 10-minute break you are likely to improve the learning outcomes (even if you have got slightly less time for teaching).
Not to offend your teaching methods or style, but perhaps you should ask yourself why the students are leaving in the first place. I would suggest talking to one of them outside of class and asking honestly if there's something you can do to help their learning experience that is non-disruptive to the other students.
I had a professor who was brilliant but not good at teaching because he had difficulties relating to his students. Because of this, several students would leave for 10-20 minutes at a time in the middle of class because they felt they weren't getting anything out of the class. If your students need more stimulation during lecture, try switching up your teaching style once in a while. Include a little bit of interactivity with trivia or jeopardy-style extra credit in the middle of class to keep everybody participating and excited to learn.