Tesla Inc. is growing faster than any other auto maker—just not always in ways stockholders would want. The company’s debt has surged just as fast as sales, while profits remain elusive.

The electric-car maker booked a record $11.8 billion in revenues last year, as it began to launch its highly anticipated Model 3 sedan, up nearly sixfold from 2013. That growth has led stock investors to bless Tesla with a $57 billion market value, which rivals much larger companies like Ford Motor Co. and General Motors Co.

CEO...