Can a tree infected with "Black Knot" be saved ?
Whether the tree can be saved depends on how serious the infection is.
All effected branches should be removed properly (making correct pruning cuts) and destroyed Immediately by burning or burying in a remote location! As always, prevention is the best policy when it comes to black knot as it is fairly common to plums and cherries. In other words, catch it before it happens.
Preventive measures are treatments with fungicides that contain any of the following: Captan, Chlorothalonil, Thiophanate-methyl, and/or Lime Sulfur. Remember whatever you may use, always follow the label directions!
Below I have listed several Extension sites that may provide further information on your problem.