If you have a dream of a dead puppy this probably means that your sense of innocence and your sense of loyalty is dying. Puppies are known for being intensely loyal to their owners and constantly tagging along with them no matter what they are doing. It can make it hard for you to really get to the bottom of things because you might think your sense of cuteness is dying, but it is really your sense of loyalty. You need to pay attention to this in yourself. If you see this happening in your life, don't let it continue. You need to find that place again in your life.
There are a lot of things that a dog might represent in a dream. Dogs are known for being loyal and for loving their owners unconditionally as long as they are fed, treated well, and not abused. If you are a good owner you will make sure that your dog is taken care of. However if you are a bad owner you might end up letting your dog die, or at least dreaming of it. Usually if you have a dream of a dog dying it means that your dog is not being well taken care of by you. You are not doing the best job of taking care of your pet even though you really should be trying harder than you are. If you have a dream in which you see a dying dog it means that you need to try your best to take better care of your dog. You are clearly worried about the fact that you may have been neglectful of your poor pup. Put a bit more effort into taking care of your beloved beast and you will see a great improvement in their treatment and in the quality of your dreams which should in all fairness, not involve dying dogs anymore.