On September 24, 2019, about 1002 eastern daylight time, a Cessna 337G, N108LS, was substantially damaged when it was involved in an accident near St. Augustine, Florida. The private pilot and designated pilot examiner sustained serious injuries. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 flight test. The pilot and examiner departed on the flight portion of the practical test for the pilot’s multi-engine rating. They conducted air work and then returned to the departure airport to perform takeoffs and landings. After landing, the pilot cleared the runway and requested with the tower controller to perform traffic pattern work. The controller indicated that there would be a delay of five to ten minutes, which the pilot acknowledged, and held the airplane short of the runway. While waiting for a takeoff clearance, the examiner questioned the pilot about the rear engine temperature, which the pilot determined was within limits. The controller subsequently cleared the airplane for an expedited takeoff. The pilot stated that all instrument indications were normal and the airplane accelerated to 85 mph then rotated. She then reported that the airplane “discontinued climbing” and shortly thereafter, the examiner assumed control of the airplane. The examiner reported that he could not land on the remaining runway; however, the airplane would not fly out of ground effect. The examiner began a left turn to land in an open area on the airport, and the airplane began to descend. He leveled the wings and slowed the airplane as it approached the touchdown area, and the airplane impacted terrain with a descent rate around 400 to 600 feet per minute. Examination of the airplane before recovery by a Federal Aviation Administration (FAA) inspector revealed that the rear propeller blades were in the feathered position, and the rear engine cowl flaps were open. The front propeller blades exhibited considerable distortion and were rotated in the propeller hub. Examination of the throttle quadrant revealed that the throttle and propeller controls for both engines were full forward, while both mixture controls were in the idle cut-off position. The airplane was recovered for further examination of both engines. Examination of the rear engine in advance of an engine run revealed no evidence of any preimpact failure or malfunction of the engine or its systems. An external fuel tank was plumbed into the airframe boost pump fuel inlet. The engine started normally without hesitation or stumbling. The engine was warmed up, then powered to 1,600 rpm, where the propeller control was cycled several times. The engine was then advanced to full power and left for about 5 minutes to stabilize. During that time, the No. 3 cylinder head temperature approached the maximum limit, and engine power was reduced allowing the engine to cool. The throttle was then advanced to full for about 1 minute and the rpm increased without hesitation or stumbling. The engine was brought back to idle for several minutes to duplicate some of the delay on the ground, then again advanced to full throttle; no anomalies were noted. The rear engine was secured using the mixture and the propeller remained in a normal low pitch position. Damage to the front engine oil filter adapter precluded operational testing of the engine. The front engine and its systems were examined, and no discrepancies were noted that would have precluded normal operation. Review of recorded engine monitor data revealed that, when power was applied for the accident takeoff, the front engine was within 100 rpm of its rated takeoff power, while at the same time the rear engine was at 137 rpm, and remained at that value for the remainder of the recorded data. Further review of the recorded data revealed that the rear engine oil temperature while on the ground awaiting takeoff clearance reached a maximum of 227°F, which was 13°F below the maximum red line value. A placard on the instrument panel stated, “Do not initiate single engine take-off.” The owner’s manual indicated that, during takeoff, it was recommended to advance the rear engine throttle ahead of the front engine throttle and to periodically monitor fuel flow and rpm throughout the takeoff. If either of these indicators was below normal, the takeoff should be discontinued immediately while sufficient runway remained. The owner’s manual also indicated that full throttle checks on the ground are not recommended.