Mitchell, who was convicted of murdering Jodi Jones, was trying to get his 20-year minimum jail term reduced.
In April last year his lawyer, Gordon Jackson QC, argued that Mitchell was only 14 when he committed the murder and that he should not have received an adult’s punishment.
But at the Court of Session in Edinburgh yesterday (Wed), Lord Justice Clerk Lord Gill, Scotland’s second most senior judge said: “It is the majority decision of the order of the court that this appeal is refused.”
Between the judge appearing in court and delivering the verdict took less than a minute.
Mitchell, who wore a plain white shirt and had his long hair pulled back in a pony tail, remained impassive throughout the hearing.
He was given a life sentence when he was convicted of murdering girlfriend Jodi Jones in Easthouses, near Dalkeith, Midlothian in 2003.
Mitchell has always maintained his innocence and in 2008 he lodged an appeal against his conviction but that too was refused.
Members of Jodi’s family were also present at court today and sat in the back row.
As she left court – Jodi’s mother – Judith Jones, said: “There is still a long road to go yet. I’m not wanting to say anything else just now.”
Soon after, Mrs Mitchell came out of court and proclaimed: “The fight goes on. It is not over.”
When asked what the next stage of the “fight” was, she replied: “You’ll see.”
Jodi Jones’ body was found bound and mutilated on a woodland path near her home.
Lord Nimmo Smith said the photos he saw of her injuries were the worst he had ever seen.