20140329006669I

The pilot-in-command (PIC) of N403GF with two passengers were on a pleasure flight from arlington municipal airport (kgky) to Houston Southwest Airport (kaxh). The PIC landed on rwy 27 at kaxh. The landing was a little long and after landing the PIC missed the first exit from the runway. He continued to slow and taxi toward the second exit. While taxiing the PIC heard another aircraft behind him announced that they were departing rwy 27. The PIC became worried that the second aircraft did not realize that N403GF was still on the runway. To prevent a conflict between the airplanes, the PIC increased his taxi speed to reach the second exit sooner. At a high rate of speed the PIC tried to turn onto the second exit; as the aircraft turned to the right the aircraft tilted to the left. The PIC stated that he thought the aircraft was going to flip over, so he released the right rudder to stop the rolling of the aircraft. The aircraft ran off the the runway on the right side, stuck a taxiway sign, went into the ditch and stopped in the mud. The nose gear was submerged in the mud. The aircraft substained minor damage. The strut on the PIC side of the aircraft had a small dent, and one of the propeller blades was bent. The dent on the sturt was caused when the aircraft hit the sign. The sign was destroyed. The pilot and passengers were uninjured.