When a STEM research topic can be studied experimentally, computationally, and theoretically, do PhD programs typically focus on only one approach? In American universities, when a STEM research topic can be studied experimentally, computationally, and theoretically, do PhD programs in this research topic only focus on one of the three approaches or a combination of the three approaches?

For instance, consider physics.  If I find a PhD program called "Experimental Physics PhD" at University X, and if I get accepted and go there for my PhD, will I miss out on computational physics and theoretical physics training...and be trained only as an experimentalist?
From my experience, such focuses are often called something like "Concentrations" or "Tracks". The intent of these programs is to allow the student with a very specific interest to tailor the program to their own interests. Again from my experience, these tracks mostly affect the courseload that a student will have. 

Students are always encouraged to network within the department, talk to other people, and if interested take seminars or possibly even full courses (if their advisor is the type to allow that sort of thing) outside of their interest, simply to learn more about their field.

Your training will consist mostly of two parts, your research and your coursework. If you choose experimental physics, your courses will be mostly related to that, and (I assume) your research will be in that field as well. The extent to which you move laterally within your field is really up to you. I think you'll find that your main enemy here is simply time; there's too much to learn and not enough time to learn it. Best of luck with that battle! :)