Magnetic plucking is an enabling technique to harvest energy from a rotary host as it converts the low-frequency excitation of rotational energy sources to high-frequency excitation that leads to resonance of small-scale piezoelectric energy harvesters. Traditional nonlinear analysis of the plucking phenomenon has relied on numerical integration methods. In this work, a semi-analytical method is developed to investigate the stability and bifurcation behaviors of rotary magnetic plucking, which integrates a second-order perturbation technique and discrete Fourier transform. Analysis through this method unfolds that the oscillatory response of the beam can lose stability through the saddle-node bifurcation and Hopf bifurcation, which eventually causes the beam to collide with the rotary host. Further, the influence of the magnetic gap and rotational speed on the stability is discussed. The study also reveals that the nonlinearity of the magnetic force can amplify the electrical power at primary resonance. As a result, the traditional impedance matching approach that neglects the nonlinearity of the magnetic force fails to predict the optimal electrical resistance. Finally, a finite element analysis shows that the instability is sensitive to damping, and the traditional single-mode approximation can lead to considerable error.