It wasn't mention in the manga or anime if Deidara even had parents, let alone if they were alive or dead.
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Deidara has no full name (which means no last name) or at least none that anyone knows of. He is simply 'Deidara'.
It is in episode 133: Clash in Naruto Shippuden but is only shown as a flash back
he had to have parents we all have parents
Hidan's Parents Aren't Mentioned.
His parents would be his mother and father.