PALMA, Mozambique—Cascata Makame only had a few moments to gather her children and a few belongings one night this month as militants raided her village in northern Mozambique, a region home to one of the world’s largest natural gas deposits.

As Ms. Makame fled, the attackers burned scores of homes, looted food and livestock and left what has become a grim calling card in this previously peaceful region: seven decapitated villagers.