Blue juice is a euphemism in veterinarian circles for the euthanasia solution administered to pets, live stock and research animals. This solution is commercially made with brilliant blue the food colouring. It contains this dye to prevent confusion with other injectable veterinary preparations.

There is a variation used for large animals such as horses with a high concentration of the Sodium pentobarbitone which is often coloured red, but the term "red juice" is not in common usage.

Further note:
As far as I know, the solution used for lethal injection as capital punishment, contains no dye whatsoever.

See Pentobarb 300 for more about this topic.