"I am sorry for the division that the events of these last few weeks have caused," Saenz-Lopez wrote in her resignation letter. "It was never my intention to bring any negative exposure to our city."
A custody hearing Monday is expected to decide who gets Puddles, who Saenz-Lopez renamed "Panchito" after taking the dog last summer.
A neighboring family accuses Saenz-Lopez of refusing to return the dog after leaving it in her care while they went on vacation. A day after her neighbors left, Saenz-Lopez called to tell them Puddles had died.
Three months later, a relative of the neighbors saw the pet at a dog groomer. When Saenz-Lopez refused to return the dog, the family filed a criminal complaint and a civil lawsuit against her.
Homero Canales, who represents Saenz-Lopez, has said his client believed the dog would die if returned to her neighbors.
Saenz-Lopez, the city's mayor since 2003, was indicted Jan. 18 on two felony counts of tampering with evidence and concealing evidence.
Those charges came after Saenz-Lopez filed a police report claiming the dog was missing. The dog was later spotted at the home of Saenz-Lopez's twin sister, in Ben Bolt, about 10 miles from Alice.
City commissioners voted unanimously last week for a resolution urging Saenz-Lopez to resign. Mayor Pro-Tem Juan Rodriguez will take over mayoral duties.
Alice is about 45 miles west of Corpus Christi.