The 2,779-hour private pilot performed a short/soft field takeoff from a dirt road that was oriented in a northeasterly direction. About 15 feet above ground level (agl) the single-engine airplane drifted to the right side of the road and the outer 12 inches of the right wing came into contact with branches from a mature mesquite tree. As the airplane yawed and banked to the right, the pilot responded by applying full left aileron and rudder to no avail. Shortly thereafter the airplane impacted terrain and came to rest in an upright position. The pilot and sole passenger were able to egress the airplane unassisted. There was no post-impact fire. The wind was reported from approximately 60 degrees at 10 knots gusting to 15 knots. The pilot reported that there was no mechanical malfunction or failure with the airplane.