Currently, self-retaining laryngoscopic surgery is not suitable for some patients, and there are dead zones relating to surgical field exposure and operation. The quality of the surgery can also be affected by the long periods of time required to complete it. Teleoperated continuum robots with flexible joints are expected to solve these issues. However, at the current stage of developing transoral robotic surgery systems, their large size affects the precision of surgical operative actions and there are high development and treatment costs. We fabricated a flexible joint based on selective laser melting technology and designed a shallow neural network-based kinematic modeling approach for a continuum surgical robot. Then, human model and animal experiments were completed by master-slave teleoperation to verify the force capability and dexterity of the robot, respectively. As verified by human model and animal experiments, the designed continuum robot was demonstrated to achieve transoral laryngeal surgical field exposure without laryngoscope assistance, with sufficient load capability to finish the biopsy of vocal fold tissue in living animals. The designed continuum robotic system allows the biopsy of vocal fold tissue without laryngoscope assistance. Its stiffness and dexterity indicate the system's potential for applications in the diagnosis and treatment of vocal fold nodules and polyps. The limitations of this robotic system as shown in the experiments were also analyzed.