Police video shows officers using tasers, at least twice, to try to stop Valenzuela, but they didn't work.
Eventually they catch up with Valenzuela and get him to the ground.
The struggle lasts for more than four minutes.
"I'm going to (expletive) choke you out," officer Christopher Smelser tells Valenzuela.
According to internal police records, Smelser used a lateral vascular neck restraint, a maneuver with a controversial history.
In a statement, the chief of the Las Cruces Police Department expressed his condolences to Valenzuela's family.
"Words are insufficient to bring comfort to Antonio Valenzuela's family, but I extend my sincere condolences for their loss," Chief Patrick Gallagher said. »