The 12-person jury had been deliberating since Wednesday, April 6.
On Tuesday, April 12, the jury told the court it could not reach a unanimous decision and a mistrial was declared.
Beckett, 59, is charged with first-degree murder in the August 18, 2010, death of his wife, Laura Letts-Beckett, who drowned on Upper Arrow Lake near Revelstoke.
The Crown has alleged Beckett killed his wife out of greed, hoping to cash in on life-insurance and accidental-death benefits.
Beckett told jurors his wife's death was either suicide or an accident.
Letts-Beckett went into the water while on an evening boat ride with her husband. She was not wearing a life jacket and was not a strong swimmer.
"With it all being circumstantial, it's hard to tell," the juror said.
"A lot of the Crown's case hinges on things that happened after the fact.
"But common sense tells you you're going to trust the system."
The juror, who was excused following a random draw to bring the number of jurors down to 12 from the precautionary 14, said Beckett did not appear to trust the system.
Beckett was combative during cross-examination by Crown prosecutor Joel Gold and had multiple outbursts during the trial.
He was warned numerous times by Justice Meiklem to remain quiet.
The juror noted many jurors laughed in court when such moments occurred.
"The outbursts, most people found it comical," the juror said.
"It was interesting. Old man yells at cloud."
- Kamloops This Week