Euthanasia for animals
Being mindful all the time is an important part of the practice. Not just at the time of death. But if you have a wholesome thought at the time of death, your next birth will be better.

Whether it's human or animal, what makes you think killing will relieve a being from suffering? It could be born in a worse place. Your action is based on a big assumption or at worst, annihilationism. 

In any case, if killing ended suffering, Lord Buddha would have preached it as the fourth noble truth, instead of the noble eight fold path. :)