Well, I'm not a vegetarian, but Miko kind of is
Because of his liver shunt, he is on Royal Canin veterinary hepatic diet. This food contains a lower amount of protein and it comes ONLY from soy and vegetables...no protein from meat at all.
So, dogs can definitely survive without meat even though they are carnivores, you just have to make sure that they're getting everything their bodies need. For example, Miko can't eat meat, but he still gets his protein and his food has the vitamins and minerals that his body requires.