Can My Cat Go Vegan?
Unlike dogs, cats are obligate carnivores and are unable to survive on a plant-based diet.
The lack of essential amino acids such as taurine, as well as arachidonic acid and vitamins A and B can cause cats to go blind, suffer from liver problems, and cause heart failure.
Feeding your cat a vegan diet is only possible if the diet is appropriately supplemented with the necessary nutrients and should only be attempted under the supervision of an experienced veterinary nutritionist.

Dogs on the other hand, the answer is a little more complicated. Read my article on Dogs and Veganism here.