The flight instructor was evaluating a pilot receiving instruction in a tailwheel-equipped, high-performance airplane for a visual flight rules cross-country flight. He added that they considered the runway to be "a one-way strip." When they arrived at the private airstrip, the GPS indicated a 5-knot crosswind from the southeast. During the approach, the airplane was about "50 ft high" when it crossed their predetermined go-around point; they continued the landing. During the touchdown, the airplane bounced twice, and the pilot then initiated a go-around. The instructor then "reminded" the pilot that they were committed to the landing and instructed him not to go-around, so the pilot transitioned the airplane back to landing. During the subsequent touchdown, the airplane "quickly" veered right. The pilot attempted to correct the veer, but the airplane exited the right side of the airstrip onto soft ground, and it then nosed down and came to rest on the spinner and left wing. The airplane sustained substantial damage to the left wing. The instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The pilot indicated that the wind at the airport was from about 140° at 5 knots. The pilot landed the airplane on runway 5. The flight instructor recommended that he should have taken the controls sooner in the abnormal situation.