What Does It Mean When My Cat Sneezes And Blood Comes Out?

You need to take the cat to the vet as soon as you can. Any bleeding is not a good sign, it could be feline leukemia if it doesn't have it's shots, or any other number of problems. Hope this helps, good luck to you and the kitty.

Feline upper respiratory complex is very common in cats.  This is caused by several viruses that break down the body's immune system and allow bacteria to invade.  Cats typically sneeze, have nasal discharge, may become lethargic or stop eating.  Blood means the nasal passage has been severely damaged or irritated by the sneezing.  
Other causes of bloody nasal discharge/sneezing are fungal infection, nasal foreign body, and cancer.
Have your cat examined by a veterinarian to determine the problem and start appropriate treatment.