Steven Doolan and Charlotte Gayter, of Grangeway, said the RSPCA put down Poppy after she ran away from home.
Miss Gayter, 23, said the couple had asked to delay collection of the dog as the family were struggling to arrange transport.
She said their car was being repaired at a garage and no-one else was available to pick up the dog.
Miss Gayter had tracked down Poppy to RSPCA Liverpool in Halewood, a day after she ran away on April 26.
Miss Gayter phoned back last week, only to discover that the dog had already been put down.
Mr Doolan, 24, who served as a private in The Mercian Regiment, lost a leg in an IED explosion bought the puppy nine months ago to celebrate the first year of the couple’s relationship,
They believe the puppy, a one-year-old Staffordshire bull terrier, escaped through a gap in a fence. It was the fourth time she had run away.
Miss Gayter said the dog was much loved by her, Mr Doolan and her two-year-old daughter.
She said the loss has ‘devastated’ the family.
She said: “The RSCPA centre tried to claim that Poppy was a nasty dog but she was such a loving pet. My daughter kept asking where she was but now she knows Poppy’s not coming back.
“The RSCPA didn’t even ring me before she was put down. I wasn’t informed. It just seems like no-one understands, that they don’t care.
“We’re all devastated.”
An RSPCA spokesman said a vet made the decision to put the dog down because it was not good around other dogs.
He said it was the fourth time a warden had handed Poppy, who was microchipped, in as a stray.