A warrant backed with bail has been issued for David Neil Savage, aged 58, of Regent Street, Long Eaton, Nottingham.
He is charged with causing unnecessary suffering to an animal.
It is alleged that he abandoned his dog in a property in Crosby after he left the island.
The dog had to be subsequently put to sleep as it is alleged that he made no arrangements for the pet to be cared for after he departed.
Prosecuting advocate Barry Swain told the court police had contacted Mr Savage, but he had claimed he was not working so he could not afford to travel to the island.
The warrant will rebail the defendant until a new court date of July 4.