It takes more than a smart premise to make a movie, but “What to Do with the Dead Kaiju?” has a good one. Satoshi Miki’s creature feature picks up where most of its predecessors end: After rampaging through the capital, a colossal kaijū (monster) has abruptly died, leaving the authorities to figure out how to mop up the mess.

At a buck-passing Cabinet meeting, it quickly becomes clear that the politicians leading the nation through this time of crisis may not be up to snuff. They assemble a group of eminences to pick a name for the deceased beast, and christen it “Hope.” When the carcass starts belching noxious fumes, they choose to refer to the effluent as “the smell of ginkgo.”

The task of disposing of the behemoth falls to Arata Obinata (Ryosuke Yamada), a member of the fictional Japan Special Forces. He’s also a man with a past: He used to date Yukino Amane (Tao Tsuchiya), now secretary to the environment minister (Eri Fuse), only to vanish three years ago in circumstances best described as paranormal.