Ashley Gill, who was 25 and from Llandudno Junction, was found unconscious in his cell at a Liverpool prison on the 29 April.
Paramedics failed to revive him. His family said he had suffered a severe asthma attack.
Two guards from Forest Bank jail in Salford, where Mr Gill was previously, put messages on Facebook.
A spokesman for Sodexo Justice Services, which runs Forest Bank prison, said: "Two employees were dismissed after an investigation."
Mr Gill's cause of death is being investigated by the independent Prisons and Probation Ombudsman.
The BBC understands the comments by the guards were posted on Facebook after news reports of Mr Gill's death in HMP Liverpool.
Two prison guards have been sacked for posting offensive messages about a Welsh prisoner who died in jail.