The jury deliberated all day Wednesday before stopping at 5 p.m.
He could face up to life in prison if jurors find him guilty of murder in the asphyxiation death of Debora Flores Narvaez during an argument at his home in December 2010.
Prosecutors say Griffith killed Narvaez because she endangered his romance with another woman.
The trial in Clark County District Court has featured lurid testimony about violence between Flores and Griffith; his ongoing relationships with several women while she sought exclusivity; and the dismemberment of her corpse before it was found in tubs of cement.
(The Associated Press contributed to this report)
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