The man, whose name has not been released, was taken in critical condition to Intermountain Medical Center, Hoyal said.
The incident prompted a 45-minute standoff with police. Pictures KUTV's Brian Mullahy tweeted from the scene also show heavily armed SWAT officers with their guns trained on an open front door.
Hoyal said officers had to persuade her to come out of the home, then they called Animal Control to remove a pit bull and another dog.
Hoyal said the stabbing and standoff occurred after the couple argued over money.
A man and two small children also left the home after the standoff. Hoyal did not immediately have information about them, but said other families also reside in the home.
The woman was to be booked into the Salt Lake County jail on suspicion of domestic violence-related attempted murder and domestic violence in the presence of a child, Hoyal said.