Trevor Wellington, 46, of Pennytinney, St Kew, Cornwall, shot the 18-month-old collie, called Jim, three times after the dog came on to his land last April.
He was found guilty in January at Liskeard Magistrates Court of causing unnecessary suffering to an animal.
On Wednesday he was ordered to do 80 hours community service and pay more than £700 in compensation and costs.
'Terrible death'
The court heard that he had a long history of arguments with the dog's owner and neighbour Jonathan Whitten.
Wellington was found not guilty on a second charge of criminal damage.
Magistrate Peter Howard said: "This has been a sad and tragic case - one which was avoidable.
"Jim died a terrible death."
The court was told Wellington had come home from a business appointment and found Jim trying to get at his daughter's pet rabbit.
After chasing the dog away he claimed he tried to send it home by shouting and stamping his feet but it would not leave so he got his gun and fired a warning shot in the air.
The court heard that when this failed to send Jim home he shot him, first in the rump area as he turned and then twice in the neck.
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