Junior Bradshaw, 31, and Kevin Liverpool, 34, are charged with conspiring to murder the singer last year.
Both men, from Manchester, England, deny charges of conspiracy to commit grievous bodily harm and conspiracy to rob.
The pair were arrested in Cullompton, Devon, on June 13, 2011 after being seen driving in the area around the village of Langford in a Fiat Punto car, several miles from Stone's home near Ashill.
The trial was adjourned by Judge Francis Gilbert in order to allow the defence team more time to explore medical evidence relating to the case, and will resume in March 2013.
It has previously been questioned whether Bradshaw would be fit to stand trial after he was moved to a mental health unit earlier this year.
Stone has previously said that she refuses to let the incident affect her life in a negative way.
She said: "There are a lot of crazies in the world. Isn't it weird? I mean what an awful thing to do. But, no, it's fine, they're just completely off their Charlie.
"It's weird because I live in the middle of nowhere, well that's why they got lost, which is good.
"I do feel very safe where I live. I live in the house that I grew up in and I don't ever plan on moving. I love my home because there's an extended family. I have four neighbours, one's a neighbour with a shotgun, and I've got a great Rottweiler.
"It's silly to worry about things that didn't happen. Just gives me more lyrics, more stories to tell."
Watch the video for Joss Stone's 'While You're Out Looking For Sugar' below: