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In the present paper, we study small data blow-up of the semi-linear waveequation with a scattering dissipation term and a time-dependent mass term fromthe aspect of wave-like behavior. The Strauss type critical exponent isdetermined and blow-up results are obtained to both sub-critical and criticalcases with corresponding upper bound lifespan estimates. For the sub-criticalcase, our argument does not rely on the sign condition of dissipation and mass,which gives the extension of the result in \cite{Lai-Sch-Taka18}. Moreover, weshow the blow-up result for the critical case which is a new result.

Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass