MOCOA, Colombia—Wilmar Benavides, 37, was one of hundreds of shattered residents milling about outside Mocoa’s cemetery on Monday.

Mr. Benavides had come to claim the bodies of his wife and 11-year-old daughter Alison, who were swept away Saturday when this city’s three rivers swelled, triggering an avalanche of rocks and trees that killed at least 273 people.

What...