Devon and Cornwall Police have identified the man as Clive Jones, 60, from Falmouth.
Jones got into difficulties while diving with other members of Falmouth Diving Club from the vessel Patrice II, about three miles off St Anthony Head.
When it was realised that he had not arrived back at the boat, divers descended to look for Jones, as the emergency services made surface and air searches.
The divers found their unconscious colleague and raised him to the surface for airlifting to hospital, where it was confirmed that he had died.
An inquest will be held.
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Cornish fatality
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