I read it as the Grissom stating "when this ship would be destroyed" which means that the Grissom text activates immediately and then Cheat Death activates "If your ship was just destroyed" meaning after the ship is destroyed.
The USS Grissom text states
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[b]WHEN THIS SHIP WOULD BE DESTROYED:[/b] The attacking ship must discard one [CREW] Upgrade. If it can't, place an [AUXILIARY] Token beside it .
Cheat Death states
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If your ship was just destroyed, discard this card to remove Damage cards 1 at a time from your Ship Card until the amount of damage is 1 point less than your Hull Value. Flip all remaining Damage Cards face down.