Radical mastectomy is a type of surgery for breast cancer that involves removing all of the breast tissue, is this true?

Yes: A radical mastectomy is an older operation that is not performed anymore. It involved removing the entire breast, the pectoralis major muscle and all of the lymph nodes underneath the arm. A modified radical mastectomy might be what you are asking about. This operation removes the entire breast along with all of the lymph nodes underneath the arm.