If a feather is cut too short, it can bleed profusely. Apply one of the following to staunch the blood flow: styptic powder, corn starch, corn flour or other flour. Apply liberally. There is a product called Kwik Stop which should be in any pet's first aid kit. It not only stops the bleeding, it contains a topical analgesic that relieves pain. I would take the bird to the vet for a checkup to make sure it will heal properly.