Tesla Inc. will be without two important executives just as the electric-car maker struggles to boost production of its first mass-market vehicle and faces doubts about its ability to raise cash.

Matthew Schwall, who was the company’s main technical contact with U.S. safety investigators as the Silicon Valley auto maker races to develop driverless-car technology, left the company for rival self-driving car company Waymo LLC. His departure comes as the National Transportation Safety Board has been investigating multiple crashes...