Euthanasia for animals Killing and harming are against the first precept. I understand that an important part of the practice is being mindful at the time of death, but do animals have this capacity?  Would it be better to end their suffering if they are dying anyway? I saw an animal suffering on the way home and this came to mind.
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. :)