To detect the presence of damage, many structural health monitoring techniques exploit the nonlinear features that typically affect the otherwise linear dynamic response of structural components with internal defects. One of them is the Scaling Subtraction Method (SSM), which evaluates nonlinear features of the response to a high-amplitude harmonic excitation by subtracting a scaled reference signal. Originally tested on granular materials, the SSM was shown to be effective for composite materials as well. However, the dependence of the technique efficiency on the testing frequency, usually selected among the natural frequencies of the system, may limit its application in practice. This paper investigates the feasibility of applying the SSM through a broadband impulsive excitation, which would avoid the need of a preliminary modal analysis and address the issue of the proper selection of the excitation frequency. A laminated composite beam was tested in intact and damaged conditions under both scaled harmonic excitations of different frequency and broadband impulsive signals of scaled amplitude. Two damage indicators working on the frequency domain were introduced. The results showed a good sensitivity of the SSM to the presence and level of impact damage in composite beams when applied through a broadband impulsive excitation.