Atomically smooth, single crystalline (Bi1-xSbx)2Te3 films have been grown on SrTiO3(111) substrates by molecular beam epitaxy. A full range of Sb-Bi compositions have been studied in order to obtain the lowest possible bulk conductivity. For the samples with optimized Sb compositions (x=0.5±0.1), the carrier type can be tuned from n-type to p-type across the whole thickness with the help of a back-gate. Linear magnetoresistance has been observed at gate voltages close to the maximum in the longitudinal resistance of a (Bi0.5Sb0.5)2Te3 sample. These highly tunable (Bi1-xSbx)2Te3 thin films provide an excellent platform to explore the intrinsic transport properties of the three-dimensional topological insulators.