What should I do if my bird has lost its wing?

Take your bird to a Veterinarian fast if you want to save the bird! I doubt it will live without care.

Welcome to Fluther.

Sad question. Depending on the bird’s species, age and general health, and of course the shock and trauma inflicted by the cat’s attack, the veterinarian may suggest putting the bird down anyway out of compassion. That is, it may not survive – or “survive well” – even with a lot of expensive care. And being a bird, it won’t be able to rationalize its suffering; it will just suffer.

Yes to the above posters advice. The shock alone of this kind of traumatic injury is enough to kill the bird and if it doesn’t die from shock it will die, soon enough, from the trauma and infection. Cat claws and saliva are very toxic to small animals/birds that are cat caught wounded.
If you cannot take it to a vet to be humanely euthanized put it in a warm, dark, quiet place and let nature take its course.