Can buy the Student Commuter Pass?

I plan to be a student in Tokyo, Japan at Sophia University. I have my Student Visa so I am eligible for the Student Commuter Pass. However, I plan to live in Yokohama and commute an hour to my university. Will the Student Commuter Pass cover the travel from my dorm in Yokohama to my university? Or will it cover part of my commute when I enter into Tokyo? Or will it cover none of the commute because I don�ft live in Tokyo?
Thank you in advance for your reply!

point 1. not all student visa holders can buy student commuter pass(es). since you are a student of Sophia University, one of accredited schools, you can buy them.
point 2. student commuter pass(es) cover the public transportation between your living address (not restricted to Tokyo) and the university, but, the route must be the shortest. you can't detour. if there are more than two routes, you have to choose one.
point 3. discount rates may vary, depending on railways and bus companies. generally speaking, if you choose the route with lesser changing of transportation companies, your total cost will become cheaper.

I have my Student Visa so I am eligible for the Student Commuter Pass.

These two things are not directly related to each other.
Generally you should be a regular student.

You had better ask your university's office
whether you really can choose a student commuter pass for your case.

I plan to live in Yokohama and commute an hour to my university.

What station on which line is close to your dormitory?

Your university has four campuses in Tokyo.
Will you commute to Yotsuya Campus?

Yes, I plan to commute from there to Yotsuya Campus. I am not yet in Japan but I know I am eligible to get the Commuter Pass. I am not sure the best route to get to the university from the dormitory.

Thank you for your help!