The problem with the categorical imperative is that you already have a set of morals which guide what you're going to select as the universal law. In this case you choose to interpret a single act of killing as if it means that thereafter murder is justified. So it's cherry picking combined with the slippery slope argument.
Another way to see it would be, for example, that it's a universal law that each time one could get a million dollars for killing a puppy, one should do it. There's no need to say that the universal law is about killing but about puppies. Or it could be about mammals, or about exactly a million dollars. Or about causing some harm to get some benefit. One must always decide what the word "universal" means, and other people are going to disagree with you. You're simply choosing a level of abstraction that's convenient to your already existing moral position, in this case indignation over thinking about a puppy being killed. There's no pure rationality when it comes to morals.
It is not the person committing the act who's submitting to a principle by which murder is always justified. It is actually you who are suggesting imposing such a principle on everyone on the basis of Kant's imperative. Is that not tyranny? I think people should be free to change their minds and adjust their opinions according to the situation. If you claim that a person killing a puppy submits in principle to having their mother killed, it just means that you are unwilling to see any differences in those two situations on the basis of your desire to have a universal rule, and that is much more worrying than someone killing a puppy for a million. You may call that desire for a universal rule logic, but I don't.