Rockburst hazards exhibit different spatiotemporal characteristics in deep tunnel excavation. Failure characteristics and energy evolution process of delayed and instantaneous rockburst of basalt rock were investigated based on single-sided unloading experiments under true triaxial conditions. High-speed photography and acoustic emission (AE) monitoring were used, and computed tomography (CT) scanning, fractal theory, and crack classification were employed for failure analysis. A three-dimensional damage model considering variable stiffness of testing machine was established to calculate the energy evolution of rock-machine system during the entire process of rockbursts. Results show that delayed rockburst includes three stages of small particles ejection, rock slab buckling, and violent mixed ejection, while instantaneous rockburst is characterized by rock slab spalling accompanied with slight particles ejection. Delayed rockburst exhibits a progressive failure mode of large-scale expansion of tensile cracks (before failure) to small-scale penetration of shear cracks (upon failure), while instantaneous rockburst shows a large-scale shear failure and abrupt penetration of shear planes upon failure. Delayed rockburst consumes less energy, and most of dissipated energy is converted into kinetic energy of ejected rock fragments, causing a higher intensity level of rockburst; instantaneous rockburst consumes more energy, but almost all dissipated energy comes from internal friction energy of shear failure, causing a higher scale of rock damage. Before rockburst failure, elastic strain energy stored in rock remains basically unchanged, while the energy stored in testing machine continuously decreases, indicating that rockburst is triggered by energy release of loading system. Energy dissipation rate (EDR) can be used as a precursory index for rock failure induced by quasi-static loading such as delayed rockburst. High EDR means damage intensification, stress drop, active AE events, and acceleration of shear crack expansion inside the rock. The findings of this study can provide new perspectives for the mechanisms and early warning of rockbursts.