SAN DIEGO—Immigration judges in this city are presenting a challenge to the Trump administration’s policy of sending asylum-seeking migrants back to Mexico, terminating such cases at a significantly higher rate than in any other court, according to federal data.

Between January and the end of September, immigration judges in San Diego terminated 33% of more than 12,600 Migrant Protection Protocols cases, also known as Remain in Mexico, according to data collected by the Transactional Records Access Clearinghouse at Syracuse...