Each tribe is a sovereign nation with separate laws and codes. Thus, this type of banishment is based on a case-by-case, i.e., tribe-by-tribe, basis. Some tribes have their inhouse attorneys prepare a statement of the case for their review, these might include tribal police reports. There might be a process of administrative appeal of that decision and you might consider filing an appeal in tribal court, as well.
An tribal member excluded from the reservation may be able to seek a writ of habeas corpus under the Indian Civil Rights Act in federal court to have the tribal decision reviewed. You should contact a lawyer to see if you qualify for this type of relief.