When cats swallow sharp bones or foreign objects, their intestines can be damaged, causing blood in their stool. If left untreated, this can lead to perforated intestines and bleeding into the abdominal cavity. This is especially common in kittens aged 1-3 months, whose digestive systems are not yet fully developed, and some owners feed them dry cat food. At this age, kittens are best fed easily digestible liquid foods such as MeowThink goat milk powder, nutritional rice cereal, Royal Canin wet food pouches, and Dr. Cat milk replacer. 
Kittens under 3 months old need internal deworming. If your kitten is over 3 months old and hasn't been dewormed yet, and is having diarrhea with blood, and you're unsure if it's parasites, you can take a stool sample to a veterinary clinic for a fecal examination. If parasites are confirmed, it will need to be treated with deworming medication such as Drontal or Coccidioidomycin.
Another possibility is indigestion, caused by overfeeding, sudden changes in feeding volume without a transition period, or feeding the cat foods it has never eaten before, especially high-protein foods.
