How Does a Vet Put a Dog to Sleep?. Part of the series: Canine & Feline Diseases. A vet puts a dog to sleep by first injecting the animal with a sedative to calm him down before giving the dog an overdose of an anesthetic, and the whole procedure is a very peaceful and humane way to euthanize. Understand the process of putting a dog to sleep with helpful information from an experienced veterinarian in this free video on pet health.

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