Dutch national Richard de Wit, 43, has pleaded not guilty to charges of murder and illegally fleeing the state.
Prosecutors presented two alleged witnesses, a murder weapon and bloodstained clothing but the judge said their evidence was inconsistent.
He adjourned the case saying proceedings would resume on 4 October.
Sarah Groves was found stabbed to death in April on a houseboat in Srinagar, where she had been living with a local family.
The two witnesses from the family were a father and his son who described himself as Sarah's boyfriend.
BBC reporter Riyaz Masroor said the judge rejected their evidence as it did not match up with the statements they had previously given.
He said the murder weapon - a broken knife - and clothes were rejected by the judge as "inconclusive evidence".
Mr Masroor said that as the case involved two foreigners there was a real push from the court and state authorities to "leave no loophole" in achieving a result.
A judge in Kashmir has rejected prosecution evidence put forward in the trial of a man accused of murdering Guernsey woman Sarah Groves.