Although a graft reaction (please note that I'm not specifying that it is a graft rejection) might have precipitated your systemic illness, it could have easily been the other way around (i.e., your systemic illness diminished your ability to tolerate the graft). In any case, I am unaware of any documented evidence that bone grafts (especially human/allografts) have led to systemic disease, although the theoretical potential of infection transmission can't be entirely ruled out. (Bone grafts are normally sterile, although true sterility depends on proper attention to the manner in which sterility is achieved.)
You do not specify the condition for which you are receiving treatment, although the reference to your body "fighting itself" implies an autoimmune disorder. Methotrexate is an immunosuppressant drug, and it is a relative contraindication for bone grafting. In other words, had you been taking methotrexate at the time your grafting was being contemplated, your surgeon probably would not have placed the graft.
In any case, the cause of autoimmune disease is not known. Although there is often a genetic component, environmental triggers are suspected of playing a role in disease flare.
Although it is normal protocol to remove a failing graft, I am unaware of any documented guidance that suggests that recommends removal of a successful graft in order to mitigate the symptoms of autoimmune disease. The rare exception to this issue is something called "graft versus host disease", which occurs after transplantation of immune cells (e.g., bone marrow transplant), but that does not apply here.
In general, bone grafts do not persist in the body, but merely form a scaffold on which the native cells of the recipient grow and replace the transplanted material. The rate at which the graft material is replaced can vary, depending on the blood supply, the size of the graft, and the metabolic activity of the recipient site, but it can be quite a while (several years) before it's entirely assimilated.