We measured the microwave surface impedance of FeSe$_{0.4}$Te$_{0.6}$ single crystals with- and without external magnetic fields. The superfluid density exhibited a quadratic temperature dependence, indicating a strong pair-breaking effect. The flux-flow resistivity behaved as $rho_f(Bll B_{rm c2})/rho_n=alpha B/B_{rm c2}$. The observed $alpha$ value of $approx0.66$ was considerably smaller than that of other Fe-based materials ($alphageq1$) and was attributed to a back-flow of superfluids remarkable in disordered superconductors. This is the first-time observation of the back-flow phenomenon caused by an origin other than the vortex pinning in multiple-band systems.
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