SAN FRANCISCO — Few people east of Berkeley, Calif., would know of Sheriff Ross Mirkarimi if it had not been for the death of Kathryn Steinle, the tourist shot this summer by a Mexican felon, setting off a national debate over immigration. But in the Bay Area’s insular political pool, the sheriff’s tenure these last four years has been tasty chum.

Days after being sworn in as sheriff of San Francisco in 2012, Sheriff Mirkarimi was arrested on domestic violence charges for grabbing his wife’s arm and faced a yearlong battle with Mayor Edwin M. Lee, who sought to have him fired. Since then, his department has been troubled by scandal, including accusations of gladiator-style jail fights among inmates.

In August, Sheriff Mirkarimi’s driver’s license was suspended after he failed to file a report about a car crash; he blamed his insurance company for the lapse. Most recently, The San Francisco Chronicle reported that Sheriff Mirkarimi, who has been barred from carrying a gun because of the domestic violence charge, had failed a shooting test; he contended that he was at the shooting range only to practice.

On Tuesday, Sheriff Mirkarimi will seek re-election against Vicki Hennessy, a veteran of the sheriff’s department and the mayor’s choice; she is known more as a bridge builder than a progressive policy maker. Among the people who have rallied to support her are her opponent’s deputies and staff members.