The defense attorneys' request stems from Kouris' reaction during a July 18 hearing when they asked to continue a preliminary hearing scheduled for the next week so a competency evaluation could be completed.
At that hearing, Kouris questioned why the defense attorneys waited until a week before the five-day preliminary hearing to ask for a competency review, since the attorneys had the case since the alleged crime was committed a year ago.
"I have to tell you, the timing to me is very, very suspicious," the judge said during the July hearing. "You claim it's in good faith; I have no reason to doubt you, except that the timing is a little problematic for me."
In their motion to disqualify, Black's attorneys describe Kouris' words during the hearing as "hostile, demeaning and humiliating and disparaged the integrity and ethics of counsel for the defendant."
The defense attorneys further argue in their motion that the judge characterized the competency evaluation as a "strategic invention" to delay the preliminary hearing, and therefore has prejudiced Black to be competent.
Prosecutors have not filed a written response to the defense's request as of Friday.
A competency hearing was scheduled for Black this week; however, it was canceled after the motion to disqualify was filed. A preliminary hearing has yet to be held.
According to charging documents, Black allegedly abducted Sierra on June 26, 2012, from her West Jordan home about one block from his own home and beat, raped and strangled her before throwing her into a nearby canal, where she drowned.
Three days later, Black was arrested on suspicion of an unrelated bank robbery.
When he was taken into custody, investigators noticed soot and debris on his clothing and hands that were similar to the materials in a field where Sierra's clothes were found.
Lab results later showed Black's DNA matched DNA found on Sierra's body, prosecutors said.
Last August, Black was charged with molesting a girl several years ago. The girl, who would have been 11 or 12 at the time, attended a sleepover with members of Black's family sometime between 2007 and 2009.
Black, according to court documents, entered the bedroom where the girl was sleeping and touched her breasts, put his hands down her underwear and forced her hands to touch his genitals. The next summer, court documents say, Black lured the same girl to his apartment and again put his hands down her pants.
Black has sent letters to The Tribune from jail in which he has maintained his innocence. He said police were looking for someone to pin Sierra Newbold's murder on, and he was an easy targe, who got caught up in the investigation.