<p>When solving multi-term time-fractional diffusion-wave equations, even if the input functions are smooth, the solutions often exhibit low regularity at the beginning of time. This non-smooth behavior can cause a deterioration in the convergence order of spectral schemes, especially when traditional polynomial-based spectral methods are used. We introduce an operational spectral collocation method based on a non-smooth mapped Legendre polynomial to address this issue while maintaining high-order accuracy. The differentiation matrices using the Legendre polynomials and the fractional integration matrices using fractional Legendre functions are utilized together with the collocation approach to overcome the low regularity of the solution. This is the first time that the operational matrix approach based on fractional Legendre functions has been used to deal with time-fractional diffusion-wave equations. To deal with the two- and three-dimensional situations of the problem under investigation, the operational matrix of the second-order derivative is extended to include the high-dimensional case as well. Three numerical examples are presented to ensure the validity and accuracy of the suggested approach and to confirm the superiority of fractional orthogonal functions over classical orthogonal polynomials.</p>