These are two separate things, so let us take them one at a time.
Burial or cremation is a benefit that depends on your plan:
This covers the burial or cremation and handling charges from the vet clinic or hospital, as long as the cause of death is not one of the policy exclusions.
Euthanasia is handled differently. It is not part of the burial benefit. It can be covered as part of your pet's vet and surgical fees, but only when it is done to relieve inhumane suffering following a covered illness or injury. If your pet is put to sleep for a reason that falls under an exclusion, it would not be claimable.