Sim, os dois estão mortos
Em Cálice de Fogo , Hagrid revela a Madame Maxime que seu pai morreu pouco depois de começar em Hogwarts:
Tiny little bloke, my dad was. By the time I was six I could lift him up an' put him on top o' the dresser if he annoyed me. Used ter make him laugh..." Hagrid's deep voice broke. Madame Maxime was listening, motionless, apparently staring at the silvery fountain. "Dad raised me... but he died, o' course, jus' after I started school.
Goblet of Fire Chapter 23: "The Yule Ball"
E em Ordem da Fênix ele soube da morte de sua mãe, alguns anos antes:
"Did you... was there any sign of... did you hear anything about your... your... mother while you were there?" Hagrid's unobscured eye rested upon her and Hermione looked rather scared.
"I'm sorry... I... forget it -"
"Dead," Hagrid grunted. "Died years ago. They told me."
Order of the Phoenix Chapter 20: "Hagrid's Tale"
Isso também é declarado ou implícito nos filmes, se isso for importante para você:
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Como Au101 observa em um comentário sobre a questão, a conversa de Hagrid com Madame Maxime no filme de Cálice de Fogo está mais ou menos intacta, incluindo a revelação de que Hagrid morreu enquanto seu filho estava na escola:
Hagrid: He was a tiny little fella, my dad. I could pick him up with one hand by the age of six and put him up on the dresser. And then he died when I was still in school.
Harry Potter and the Goblet of Fire (2005)
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Embora não seja declarado abertamente, o Hagrid implica em Ordem da Fênix que a mãe de Grawp - e, portanto, sua mãe - está morta (ênfase minha):
Hagrid: I couldn't leave [Grawp], because...because he's my brother.
Ron: Blimey.
Hagrid: Well, half brother, really.
[...]
Hagrid: You will look after him, won't you? I'm the only family he's got.
Order of the Phoenix (2007)