I Cut a Piece of my Nose off and Doctor Stitched It Back on and Now Starting to Look Black is It Dead or Can I Save It? (photo)

From your picture, I would say that it is highly unlikely that the black area on your nose will be saved.  This does not necessarily mean that the nose will look bad after it heals.  I would contact the surgeon who performed your surgery so that you can be closely followed and treated to help give you the best outcome.  

Unfortunately, the photo shown implies a poor prognosis of tissue survival.  Hyperbaric oxygen treatment and/or application of leaches might be of some benefit depending on when the injury occurred.  If this area does slough, there are reconstructive options (multiple stages) which can be utilized.

At this point the tissue that was sewn back on your nose
does look compromised, but it still has some coloration in the center. It is
often amazing how much of this replanted skin can survive. Most physicians are
very conservative in their care with this by just doing dressing changes,
keeping it clean and preventing infection. It will continue to resolve on its
own and has a good chance of looking remarkably normal if cared for properly at
this point.