Team Logo. The San Diego Jaws were a team in the North American Soccer League (1968-1984). They finished last in their only season. In 1977 they moved to Nevada and became the Las Vegas Quicksilvers. Retrieved from "https://prosportsteams.fandom.com/wiki/San_Diego_Jaws?oldid=16060" Categories: NASL (1968-1984) Teams Teams in California Teams in San Diego Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.