Depending on pup's age, its so severe with young ones on dehydration, the green is bile dumping into stomach, because the stomach is empty, bile goes into stomachs to help churn the food and send on down to the intestines, this is not good.
Could have Distemper, need to know that first off, and got to go to vet...puppies showings signs of vomiting down the yellow/then greenish/brownish, need to be check for distemper,,,,,distemper can take a puppy's life...
Has your pup got fever???