Beggs, 47, was convicted in 2001 of murdering and dismembering Barry Wallace, 18, in Kilmarnock in December 1999. He was given a life sentence and ordered to serve a minimum of 20 years.
Although he lodged an appeal within days of his trial, there were numerous hearings and delays before an appeal was heard and a judgment issued in March last year. All grounds of appeal were rejected.
Beggs then asked the Court of Criminal Appeal to reduce his sentence because, he claimed, his right to have the case determined within a reasonable time had been breached. He also applied to the European Court of Human Rights in Strasbourg for damages.
In yesterday's judgment, Lord Hamilton, the Lord Justice-General, sitting with Lords Reed and Emslie, said Beggs and his legal advisers could be blamed for some of the delay.