Please do not throw the cat out! Doing so will do absolutely nothing to bring back your poor birdie! If you really decide you no longer want the cat, look for a good home for it instead of sentencing it to a potentially agonizing death! It's not the cat's fault it's a cat. My dogs would not hesitate to kill my birds and while I would be absolutely devastated if it happened, I would never throw my dogs out! I make sure my dogs cant touch my birds. I have three terrier mixes and terriers are bred to hunt. Two out of three of my terriers, one in particular, can hop up onto counters and high spaces. Theyre very cat like! The cat could be shot, posioned, beaten, run over or eaten! It could even be captured to be used as bait or snake food! You, as a pet owner, have a responsibility to the cat, regardless of what it did. You took the cat in, you decided to take responsibility for it. I dont want to be harsh, but as an animal lover and owner I am absolutely horrified that you would throw the cat to the unknown. Please find a new home for the cat if you must, do not simply kick it out. In the long run, letting a cat roam outside kills more birds and other animals. Feral cats decimate wild populations and are driving species to the brink of extinction. If you can't do it for the cat's sake, do it for the environment's.
Now that that's off my chest, I truly am sorry for your loss. My birdies mean the world to me so I can't even imagine the pain you're going through.