The bench chairman at Chesterfield Magistrates Court said: “It’s a sad thing to have to do - but some dogs are dangerous and are very difficult to rehome”.
Members of the bench had hoped to apply for a contingent destruction order - which normally sets out criteria such as keeping the dog muzzled to avoid it being put down.
However they were advised by a prosecutor that destruction was the only option as ownership of the dog - named Prince - had been transferred to the police and he was not eligible to be rehomed.
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Prosecutor Becky Allsop described how on September 25 last year the Dachshund - named Winney - was passing a garden in Bolsover when its owner saw “a female with two dogs”.
Ms Allsop said: “They ran to the bottom of the garden and the Staffordshire Bull Terrier burrowed its way under a plastic fence and went for Winney.
“It bit Winney around the neck - (Winney’s owner) tried to separate the dog from her.
“The dog was flying around. She separated the dogs but suffered bites to her fingers.”
The prosecutor said Prince had only been in his owner David White’s care for “about a week” when the attack happened.
The dog had belonged to White’s partner’s daughter, who no longer wanted him.
She said: “Mr White was watching TV in the front room at the time and did not see the incident.
“Ownership of the dog has been transferred to the police and they are seeking a destruction order.”
Paul Green, defending White, said his client had “no objection” to the dog being destroyed.
A magistrate said: “It’s a sad situation really. Luckily there were no serious injuries - we know that an out-of-control dog can wreak havoc.
“We agree with the request of the police and the prosecution that this dog be put down - it’s a sad thing to have to do.”
White, 68, of Hassop Road, Staveley, admitted being in charge of a dangerously out of control dog.
He was fined £80, made to pay £85 court costs, a £34 victim surcharge and £100 compensation.