Stewart, 38, has been charged with aggravated murder for the fatal shooting of Weber Morgan Narcotics Strike Force agent Jared Francom, 30.
Weber County prosecutors have said they plan to seek the death penalty for Stewart.
The strike force agents were attempting to serve a no-knock search warrant on Stewart's Jackson Avenue home on the night of Jan. 4, 2012, when a shootout erupted between Stewart and the officers.
Stewart is also charged with seven first-degree felony counts of attempted aggravated murder for allegedly trying to kill other officers, and one second-degree felony count related to alleged marijuana cultivation. Stewart has pleaded not guilty on all counts.
In the motion, Stewart's lead defense attorney Randall Richards notes that the death penalty may be imposed only if the jury finds that the aggravating factors of the crime outweigh the mitigating factors.
But, given that murder "is conceivably the single most egregious act known to man. The weight ... of the ultimate evil act would by its very nature outweigh any possible mitigation," the motion states.
The upshot, Richards argues, is that the Utah Legislature has enacted a law where a life sentence is only allowed "through an act or series of acts that are impossible to achieve. Therein lies the due process and cruel and unusual punishment violations of requiring the criminal defendant in a murder case to save his life only by establishing something that is impossible to establish."
Typical arguments in favor of mitigation include that the defendant is youthful, has little or no prior criminal history, or was under the influence of an emotional or mental disturbance.
But "the defendant does not believe those mitigating circumstance ... outweigh the aggravation of murder," Richards writes.
"To suggest that any criminal defendant could set forth any single or combined mitigating factors in an effort to overcome the aggravation of murder is simply illusory," the motion states.
Richards notes that while prosecutors may argue that various Utah juries have awarded life sentences in capital murder cases, "the defense believes that these are unusual examples and are in essence a jury nullification of a mandatory death sentence."