Kevin Sweat attacked his attorney, Peter Astor, with a razor blade in 2014 as he arrived at court to be sentenced for killing 11-year-old Skyla Whitaker, 13-year-old Taylor Paschal-Placker and 23-year-old Ashley Taylor.
Sweat pleaded guilty to the murders in exchange for prosecutors not seeking the death penalty.
The Oklahoma Court of Criminal Appeals on Thursday denied Sweat's appeal in the attack on Astor.
Sweat had argued there was insufficient evidence and that the judge should have recused.
A spokeswoman for the state attorney general said it isn't clear how Sweat obtained the razor blade.
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