Reattachment of fingers is a complex procedure and the chances of success depends on many factors like duration of injury, amount of contamination​, vascularity, condition of the amputed part etc. In most cases a finger cannot be reattached after more than 6 to 8 hours have passed. Even if you go to hospital immediately there are only few centers where this surgery can be done. Even with best surgery at best possible time the functional recovery may not there. However you can always try for the best possible treatment.