What to do if you accidentally cut the quick on a cat:
1. Soap
If you accidentally cut your cat's quick while trimming their nails, immediately use a cotton ball to stop the bleeding. At the same time, minimize your cat's movement to prevent further bleeding. Then, hold the bleeding nail at a 90-degree angle to a dry bar of soap and push firmly, allowing the nail to penetrate about 3 to 4 millimeters into the soap, forming a plug to seal the wound. (If a plug doesn't form, repeat the process, pressing the nail into the soap until no more blood seeps out.) It will usually fall off on its own after a few hours, and then there's nothing to worry about. 
2. Potassium permanganate
Keep Elizabeth as still as possible. Potassium permanganate is a common household disinfectant (potassium permanganate powder can be bought at pharmacies) and also has a disinfecting effect on wounds. Pour potassium permanganate powder onto a cotton swab tip moistened with water, and quickly apply pressure to the bleeding area with the cotton swab. Wait 30 seconds, and do not let the animal move around during the bleeding process. (If the bleeding does not stop, the owner can repeat the above process and apply pressure to the bleeding area with the cotton swab for 5 minutes.)
3. Pet hemostatic powder
The ingredients of hemostatic powder are generally traditional Chinese medicine preparations and talcum powder. It has certain disinfection and anti-inflammatory effects. Simply press the hemostatic powder lightly onto the bleeding site until the bleeding stops. It can also be used for minor bleeding in other places besides the nail.
4. Seek medical attention promptly.
If the cat continues to bleed heavily from the blood vessel after the bleeding has been stopped, it should be taken to a veterinary hospital for treatment as soon as possible.