At approximately 14:00 CST, a Beech BE-95 was substantially damaged when it veered off the runway during a practice engine failure on takeoff maneuver at the Mesquite Municipal Airport. Neither occupant was injured. the instructor said that, after the student applied takeoff power, the instructor covered the mixture controls with a plastic checklist, and pulled the right engines mixture lever to idle cutoff. The student was not able to maintain directional control, and before the instructor could take the controls, the aircraft departed the runway on the right side onto soft, muddy ground. The nose gear collapsed, the left propeller struck the ground, and the fuselage buckled.