<p>During deep and ultra-deep drilling, the drill-string system is prone to dynamic instability and stick-slip vibration owing to the combined effects of its slender structural characteristics and the bit-rock interaction. To reveal the underlying stick-slip dynamics, a unified dynamic modeling and stability analysis framework is developed. The bit-rock interaction model is first extended by incorporating full and partial blade configurations, non-uniform distribution, nonlinear wearflat contact, and dry friction, together with a compatible cutting-depth solution method. On this basis, an axial-torsional coupled spatiotemporal dynamic model is established, and a multiple-delay stability analysis framework is developed based on the linearization theory of time-delay systems. The proposed model is validated against field data and representative benchmark cases. The results show that the structural parameters of the bit significantly affect the system stability domain, and that appropriate blade-parameter design can improve local stability. Pronounced axial-torsional coupling and depth-dependent response evolution are exhibited by the drill-string system. Marked differences are observed between the axial and torsional responses in frequency distribution and spatiotemporal strain evolution, while the axial response further exhibits broadband, multimodal, pulse-like high-frequency excitation and traveling-wave propagation characteristics, whereas the torsional response is mainly governed by low-frequency stick-slip vibration. The present study provides a theoretical basis for bit-parameter optimization and drill-string vibration mitigation.</p>