The left main entry door departed the airplane when the pilot opened the door during flight. The pilot reported that after departure he noticed a carpet strap was hanging out of the left door and flapping against the airplane. He turned on the autopilot and decided to open the door in order to pull the strap inside. He reported he was unable to hang on to the door and it departed the airplane. The pilot reported he needed stitches because the door was ripped from his hand. The pilot contacted the departure airport stating he was returning to land, but then decided to continue the flight to an airport which was approximately 60 statute miles away where there was a certified Columbia service center. The airplane was landed without incident. Examination of the airplane revealed the door contacted and punctured the right wing. It then contacted and punctured the right horizontal stabilizer. The emergency procedures section in the pilot operating handbook (POH) contains a warning which states, "Do not open the cabin doors in flight. The air loads placed on the doors in flight will damage them and can cause separation from the airplane. A damaged or separated door will alter the flight characteristics of the airplane and possibly damage other control surfaces." The POH also states the following warning in the Doors section of the Description of the Airplane and Systems section: "If the red 'Door Open' annunciator light is on or the aural warning is playing, then one or more doors are not properly secured, and the airplane is unsafe to fly."