David Savage, 44, of Warrington, admitted owning a dog dangerously out of control in a public place at Halton Magistrates' Court.
Magistrates gave him an eight-week jail term, suspended for a year, and ordered his dog be destroyed.
Gemma Antell, the owner of the Pomeranian dog Elvis, who died, said: "Nothing is going to bring him back."
Elvis was being walked by Mrs Antell's mother-in-law when he was attacked in a garden on Kingsway South, Warrington, on 6 July.
Savage's dog was being walked by Susan Campbell, 44, of Warrington.
She appeared in court charged with being in charge of a dog dangerously out of control and is due to attend a further hearing on 7 October.
Savage was told by magistrates he must take part in an alcohol treatment plan and pay the victim Â£300 compensation.
He is also banned from keeping dogs for 10 years.
Mrs Antell attended the sentencing hearing on Monday and wrote on Twitter she "cried her eyes out".
She added: "I had to tell my distraught kids. I had to take his decapitated dead body to the vets.
"They should realise the hurt they have caused."
A man has been given a suspended jail sentence after his Staffordshire bull terrier decapitated a smaller dog.