The two were on trial for the death of James Boyd, a homeless man who was shot and killed in March 2014. Video of the shooting from one of the officers' body cameras ignited outrage in the community.
The case is one of a handful of fatal police shootings in recent years to capture national attention, sparking protests coast to coast amid a growing debate about law enforcement's use of deadly force.
Perez and Sandy faced charges of second-degree murder, voluntary manslaughter and aggravated battery. If convicted on the most serious charge they could have gotten 15 years behind bars.
On Tuesday, Judge Alisa Hadfield said the jury was split, with three jurors deciding the officers were guilty and nine believing they were not guilty.
"Based on this information, the court finds that there's no reasonable probability that the jury can agree and I'm going to conclude this proceeding by declaring a mistrial," Hadfield said in court.
Special prosecutor Randi McGinn said it was his job "to seek justice for the dead, in the hopes that it will make the living safer in the future. That's what we did."
"My job was to tell the truth and expose the truth... And then it was up to the jury to decide whether there was a criminal act or not," he added.
"Nobody, even police officers, should be above the law. And nobody, even a mentally ill homeless camper, should be below its protection."
What happened the night James Boyd died
The moments before and after Boyd was shot and killed have been watched over and over. A body camera worn by Perez recorded the police officers' fatal shots.
Dozens of law enforcement personnel had responded to 911 calls and converged on Boyd, who friends say was camping illegally in the foothills of Albuquerque. The city's homeless shelters had closed for the night.
Boyd, 38, who had a history of mental illness and who had bounced between mental facilities, jail and homeless shelters over the years, is seen on police video refusing to obey officer commands to leave the hillside.
According to court documents, he threatened violence toward police multiple times during the hours-long standoff and is heard on video recorded by a bystander saying, "I'm going to hunt you down and kill you."
The body cam shows Boyd with two small camping knives in his hands as police move closer to his makeshift campsite on a small nest of rocks.
Suddenly, things get chaotic. Boyd appears to step toward the officers. Police fire a stun grenade, then a police K9 and his handler rush forward. A few more seconds pass before Boyd turns his back, just as multiple gunshots are fired.
Boyd falls to the ground. While he is lying on his stomach, still holding the knives, the police dog goes for his legs as officers fire beanbag rounds at him. Boyd can be heard wheezing for breath.
A coroner ruled Boyd's death a homicide. An autopsy showed he was shot three times, including in the lower back and both arms.
Albuquerque police and 'excessive force'
Boyd's case ignited a firestorm in Albuquerque and focused national attention on other shootings by police officers in the city.
He was the 26th civilian shot and killed by Albuquerque police officers since 2010, a per capita rate of officer-involved deaths that was higher than New York City and Chicago for the same period.
Sandy and Perez were the first Albuquerque officers to be prosecuted for killing someone in the line of duty in more than 30 years.
The Albuquerque Police Department is currently under the supervision of the Department of Justice for excessive use of force violations.
Will the pair go to trial again?
It's not clear if the two officers will face another trial.
Raul Torrez, who is expected to be the new district attorney for Bernalillo County come January 1, 2017, (he's running unopposed), said it's an extremely important case and he doesn't want to rush a decision.
"Any decisions on the path forward must be guided by the law and the facts, and that's exactly what I intend to do with every case when I am district attorney," he said in a statement.