On December 15, 1998, approximately 1400 central standard time, a Beech BE-95-A55 twin engine airplane, N6DL, was substantially damaged when it veered off the runway during a simulated engine failure on takeoff maneuver [V1 Cut], at the Mesquite Municipal Airport, Mesquite, Texas. Both occupants, the commercial pilot-in-command [instructor] who was giving instruction and the commercial pilot who was at the controls receiving multi-engine instruction [student], were not injured. Visual meteorological conditions prevailed and a flight plan was not filed for the Title 14 CFR Part 91 instructional flight [The instruction was being administered under the guidelines of Title 14 CFR Part 61]. The flight originated from the Mesquite Airport about 1315, and had completed about 7/10ths of an hour of uneventful flight training prior to the accident. The aircraft was jointly owned and operated by the occupants. The pilot-in-command provided the NTSB investigator-in-charge with a written statement that outlined the events of the accident. A telephone interview with the pilot-in-command was also conducted. The pilot-in-command [instructor] stated that the pilot receiving instruction [student] taxied the airplane to runway 17 [6,000 feet long & 100 feet wide], performed the takeoff checklist, and commenced the takeoff roll. After assuring that full power had been applied, the instructor covered the mixture controls with a plastic checklist, and pulled the right engine's mixture lever to the "idle cutoff" position. The student was not able to maintain directional control, and before the instructor could assume the controls, the aircraft departed the right side of the runway onto soft, muddy ground. Subsequently, the nose gear collapsed, and the left propeller struck the ground. According to data provided in NTSB Form 6120.1/2, the instructor had a total of 2,788 hours of flight time, of which, 324 hours were in multi-engine airplanes, and 312 hours were in the accident airplane. He holds a commercial pilot certificate with ratings in single and multi-engine airplanes, and a flight instructor certificate with instructor ratings in both single and multi-engine airplanes. The student pilot had a total of 1,887 hours of flight time, of which, 4.7 hours were in multi-engine airplanes. He holds a commercial pilot certificate with ratings in single engine airplanes (land & sea), and a flight instructor certificate with an instructor rating in single engine airplanes. Examination of the airplane by a FAA airworthiness inspector revealed that the fuselage was buckled just forward of pilot's [left] windshield.