In this paper, we propose a novel biomechanics-aware robot-assisted steerable drilling framework with the goal of addressing common complications of spinal fixation procedures occurring due to the rigidity of drilling instruments and implants. This framework is composed of two main unique modules to design a robotic system including (i) a Patient-Specific Biomechanics-aware Trajectory Selection Module used to analyze the stress and strain distribution along an implanted pedicle screw in a generic drilling trajectory (linear and/or curved) and obtain an optimal trajectory; and (ii) a complementary semi-autonomous robotic drilling module that consists of a novel Concentric Tube Steerable Drilling Robot (CT-SDR) integrated with a seven degree-of-freedom robotic manipulator. This semi-autonomous robot-assisted steerable drilling system follows a multi-step drilling procedure to accurately and reliably execute the optimal hybrid drilling trajectory (HDT) obtained by the Trajectory Selection Module. Performance of the proposed framework has been thoroughly analyzed on simulated bone materials by drilling various trajectories obtained from the finite element-based Selection Module using Quantitative Computed Tomography (QCT) scans of a real patient's vertebra.