In one of the first moments of “Underground,” a new cable drama about the underground railroad, the camera tracks a slave played by Jurnee Smollett-Bell as she sprints through a plantation mansion to assist with an emergency childbirth. The swooping shot, captured with a drone-mounted camera, is set to pounding drums, echoing a Kanye West song that accompanied a previous chase scene.

Despite the subject matter, the makers of “Underground” are trying to subvert expectations of a somber period piece loaded with historical figures....