This paper proposes a novel idea by integrating a torsion dynamic vibration absorber with a triboelectric energy harvester to realize synchronous torsional vibration suppression and energy harvesting in a rotor system. The most fantastic feature of the proposed torsion harvester-absorber system (HAS) is the quasi-zero-stiffness (QZS) characteristic for suppressing and harvesting low-frequency vibration energy. The QZS characteristic is realized by combining negative stiffness magnet couplings (NSMC) in parallel connection with a pair torsion coil spring. A theoretical model of the NSMC is established based on the equivalent magnetic charge method, and parametric studies are conducted to provide a guideline for the design of the NSMC. Furthermore, the dynamic model of the host oscillator with a torsion QZS HAS is established based on Lagrange’s equation, and then the dynamic amplification factor is obtained using the harmonic balance method. The effects of geometric parameters on both the performances of vibration mitigation and energy harvesting are investigated. Finally, the parameters of the torsion QZS HAS are optimized using H∞ optimization method and genetic algorithm, respectively. This enables the torsion QZS HAS to effectively suppress low-frequency vibrations of the rotor system while simultaneously harvesting energy over a wide frequency band.