At about 6 a.m., deputies responded to a residence at 486 Vaughn Ave. near Scott Street, sheriff's Lt. Ed Wise said.
A 35-year-old woman had dropped her children off at a day care center located at the private residence at that address. After she left the home, she got into a confrontation with her estranged husband in the front yard. The couple was yelling and screaming and their 8-year-old child came out and tried to help break up the parents, Wise said.
During the conflict, the father, Adolfo Espinosa Valencia, cut himself with a knife and then slashed the mom's throat, Wise said. He fled before deputies arrived.
The mother was taken to a local medical center's trauma unit, where she was listed in critical condition, he said.
The couple's three children were taken into protective custody.
The 43-year-old suspect is thought to be driving one of the family's vehicles, a light gray 1995 Ford van with license plate No. 5E55168, Wise said.