I need help writing a thesis statement for this short story. I have the idea of discussing survival but I don't know what to talk about in the three body paragraphs.
I think that you are on the right track with survival being the thesis statement topic. The heart of the story is definitely focused on the theme of survival.
Thesis statements can be written in a variety of ways, but I always stress to my students two main types. The first would be a "statement, reason, reason, reason" thesis statement. That kind works well for your essay, since you have stated that it needs to have three body paragraphs. Each reason would be its own paragraph. Your statement could be "Rashmon clearly shows the theme of survival through A, B, and C." It's up to you what A, B, and C are. I would definitely use the unnamed man and woman. They both clearly illustrate that survival is more important than a supposed honorable death.
The other type of thesis statement that you could use is what I call the "point/counterpoint" style. This is where you state one idea with the intention of disproving it with your main argument. I recommend starting this kind of thesis with the word "although." That word immediately alerts your reader to a two part statement. The first part is what you don't agree with. The second part is what your argument is. For Rashmon, you might try something like this: "Although the story seems to indicate that the unnamed man is attempting to pursue honorable survival, his actions clearly indicate that he is a dishonorable survivor."
I believe that the second kind of a thesis statement is a stronger thesis, because it forces you, the writer, to admit possible reader arguments and disprove them. If you are limited to exactly three paragraphs though, go with the first thesis form.