We show Shubnikov-de Haas (SdH) oscillations in topological insulator (Bi_xSb_1-x)₂Te₃ flakes whose carrier types are p-type (x = 0.29, 0.34) and n-type (x = 0.42). The physical properties such as the Berry phase, carrier mobility, and scattering time significantly changed by tuning the Fermi-level position with the concentration x. The analyses of SdH oscillations by Landau-level fan diagram, Lifshitz-Kosevich theory, and Dingle-plot in the p-type samples with x = 0.29 and 0.34 showed the Berry phase of zero and a relatively low mobility (2000-6000 cm² V^-1 s^-1). This is due to the dominant bulk component in transport. On the other hand, the mobility in the n-type sample with x = 0.42 reached a very large value ∼17 000 cm² V^-1 s^-1 and the Berry phase of near π, whereas the SdH oscillations were neither purely two- nor three-dimensional. These suggest that the transport channel has a surface-bulk coupling state which makes the carrier scattering lesser and enhances the mobility and has a character between two- and three-dimension.