One approach to vibration control is to apply a force to a primary structure that opposes the excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear-tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap-through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap-through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may generate adverse constructive forces that substantially reinforce the applied excitation, primarily at lower frequencies. However, both analyses and experiments indicate that such high-orbit dynamics may be largely destabilized by increased bistable attachment damping. Destructive forces, which substantially oppose the excitation, are unique in that they lead to a form of vibration attenuation analogous to strictly adding damping to the host structure, leaving its spectral characteristics largely unaltered. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis, which render similar attenuation effects.