Cats Snot Has Blood. It is also possible that a nosebleed. It sounds to me like this blood is coming from your cat’s colon.

Feline viral rhinotracheitis is a respiratory disease which, although affecting the cat's breathing, can lead to serious nose and eye discharge. If your cat has a blood clot it is likely that it has lost some of its blood circulation. Sneezing blood can be caused by a blood problem, such as a clotting disorder, high blood pressure or anemia which leads to low platelet counts.