The airline transport pilot, with a hunting client aboard, was departing from a soft, 900-foot long, mud and gravel-covered off-airport site that had an area of standing water near the departure end. During the takeoff run, the pilot said he was able to get the airplane airborne before reaching the area of standing water, but as the airplane began to climb, it struck a stand of trees at the departure end of the site. The airplane sustained structural damage to the wings, fuselage, and horizontal stabilizer. The pilot said that there were no preaccident mechanical anomalies with the airplane.