Low-frequency perpendicular electromagnetic fluctuations and energy transport in multi-ion-species plasmas are studied theoretically and numerically. In thermal equilibrium, the amplitudes of heavy-ion cutoff modes, whose frequencies are slightly higher than the heavy-ion cyclotron frequencies, can be comparable to that of the magnetosonic mode. The heavy-ion cutoff modes can cause damping of the magnetic fluctuations. Long time evolution of a macroscopic magnetic disturbance is also investigated with particle simulations. It is demonstrated that the disturbance is damped more quickly than the prediction of the linear theory. Owing to the damping, ion kinetic energy is increased.