CHILAPA, Mexico — For nearly a week, gun-toting masked men loyal to a local drug gang overran this small city along a key smuggling route. Police officers and soldiers stood by as the gunmen patrolled the streets, searching for rivals and hauling off at least 14 men who have not been seen since.

“They’re fighting over the route through Chilapa,” said Virgilio Nava, whose 21-year-old son, a truck driver for the family construction supply business, was one of the men seized in May, though he had no apparent links to either gang. “But we’re the ones who are affected.”

For years, the United States has pushed countries battling powerful drug cartels, like Mexico, to decapitate the groups by killing or arresting their leaders. The pinnacle of that strategy was the capture of Mexico’s most powerful trafficker, Joaquín Guzmán Loera, better known as El Chapo, who escaped in spectacular fashion last month from a maximum-security prison.

And while the arrests of kingpins make for splashy headlines, the result has been a fragmenting of the cartels and spikes in violence in places like Chilapa, a city of about 31,000, as smaller groups fight for control. Like a hydra, it seems that each time the government cuts down a cartel, multiple other groups, sometimes even more vicious, spring up to take its place.