To begin, be aware that the most common fresh asparagus side effects are vomiting and diarrhea. When your dog is fed fresh asparagus, he may experience flatulence. If you’re feeding fresh asparagus to an adult dog for the first time, start slowly. While it is true that cooking reduces the nutritional value of most vegetables, a dog is unlikely to enjoy the taste of fresh asparagus. As a result, the best way to feed asparagus to your dog is to add cooked and pureed asparagus to home-cooked dog meals or regular dog food.