Mr Vincent Connolly pleaded guilty to the charges yesterday at Londonderry Magistrates Court.
Investigations revealed that the tails had not been docked by a certified veterinary surgeon.
He was fined £750 and was ordered to pay costs of £169.
The council has said it will continue to clamp down on irresponsible or neglectful animal owners.
Commenting after the proceedings, a spokesperson for Derry City and Strabane District Council, said: “Council gives a high priority to the welfare of domestic pets and horses and operates a rigorous enforcement policy to ensure full compliance of regulatory requirements.
“Complaints are investigated thoroughly and where necessary formal action is taken, which may include the service of Improvement Notices or, in extreme cases, the seizure of animals.
“The Council may also prosecute for offences such as this particularly harrowing case in relation to tail docking, which I hope serves as a warning to anyone who does not take appropriate care of animals.”
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