For copper miners Southern Copper Corp. and Vale SA, surging prices of byproducts like gold and silver are creating an unusual situation: The cost of producing the red metal has turned negative.

Southern Copper reported a cash cost, net of revenue earned by selling byproducts, of minus 11 cents a pound in the January-to-March period, versus 77 cents a year earlier. That means the company is making money just by extracting copper ore from mines, even before accounting for the selling price of the metal.