LEIPZIG, Germany—As Porsche maneuvers deeper into the markets for SUVs and sedans, it is racing to remind a new generation of drivers what gave the brand its original mystique—speed.

The brand has unnerved purists in recent years, first with the launch of its hulking Cayenne sport-utility vehicle, then a four-door sedan called the Panamera. Though the expansion has boosted the Volkswagen AG-owned car maker's sales by nearly 50% over the past four years, the Cayenne and Panamera made up roughly three-quarters of its 143,000...