OAKLAND—The Oakland Police Department is down to 650 officers from 800 a year ago. With the cutbacks, the department says it is struggling to maintain law and order in high-crime neighborhoods like East Oakland.

A year ago, about eight officers patrolled the area near the eastern border of the city, a roughly 10-square-mile zone. Today, during most shifts, just three officers walk the beat in the neighborhood, which is known for its drug problems and prostitution. On some days, there are so few officers...