BE55 pilot reported engine failure during the takeoff roll and attempts at vacating the runway with one engine inoperative.

Narrative

A BE55 Beech Baron multi-engine aircraft had a left (critical) engine failure at full power shortly after brake release on takeoff. The first indication of any malfunction was an abrupt and hard left yawing motion. Both engine throttles were immediately brought back to idle while simultaneously applying right rudder and maximum braking. These inputs resulted in the aircraft stopping approximately 20 feet left of centerline with the nose pointing approximately 45 degrees to the left of centerline. The left engine spooled down to zero RPM while the right engine remained at idle and the left mixture was brought to off. Initial attempt to taxi straight ahead single engine using rudder; nosewheel steering; and differential braking was unsuccessful due to the imposed yaw from the right engine. There were no abnormal indications on the failed (left) engine and so a normal restart was attempted to expedite clearing the active runway. The restart was unsuccessful and a second attempt to taxi off the runway was done by allowing the nose to continue to yaw to the left to complete a 180 degree turn and back taxi on the runway while building up enough speed to maintain directional control to complete an additional 90 degree right hand turn and clear the runway. Once clear of the runway the aircraft could not be directionally controlled during a second right hand turn and so it was brought to a stop. To facilitate taxiing back to base; a second attempt to start the left engine was initiated. This second restart resulted in visible vapors coming from the left engine. Based on the vapor; all fuel was secured to both engines and the aircraft was towed back to the line.Pilot training involving repetitive action review rendered the initial pilot motor skills to safely stop the aircraft instinctive and expeditious. The importance of continuously reviewing procedures to increase human performance to react to these types of situations cannot be overemphasized.The event was conducted with a single rated pilot at the controls and two aeronautical engineering students in the aircraft. Throughout the event the students and tower control were extremely timely and pertinent with feedback and comments. Working as a team regardless of background; training; or location was critical to preventing the event from compounding.After the aircraft was safely stopped on the runway there was a possibly an unwarranted perception by the pilot of the time criticalness to clear the active-duty runway. Winds were approximately 10 kts with an off-duty runway available that airborne traffic could have utilized to safely land.After the aircraft was safely clear of the runway the pilot contacted ground control and discussed options to have the aircraft towed back to the line. All known maintenance facilities were closed for the day and so there was an expected long delay to locate a tug. This conversation swayed the pilot to try one more start on the failed engine which resulted in vapors coming from the engine. The decision to attempt a second start when there were no current safety concerns with the aircraft state was flawed and could have resulted in creating a second unsafe situation for both equipment and personnel. The aircraft should have been shut down regardless of the expected delay for a tug.