The incident happened around 1 p.m. PT when the pug's owner was approached by a woman, who was walking her pit bull in the beach park.
But when the dogs approached each other, the larger pit bull suddenly bit down on the neck of the smaller dog. Unable to separate the animals, the pug's owner killed the pit bull using a folding knife he was carrying.
The pug was rushed to a veterinary hospital for stitches to its neck. Animal control officers also attended the scene.
Police say they are speaking to both dog owners and both are co-operating with investigators. No charges are being considered.