Negative　magnetoresistance　(MR)　is　not　only　of　great　fundamental　interest　for　condensed　matter　physics　and　materials　science,　but　also　important　for　practical　applications,　especially　magnetic　data　storage　and　sensors.　However,　the　microscopic　origin　of　negative　MR　is　still　elusive　and　the　nature　of　the　negative　MR　in　magnetic　topological　insulators　has　still　not　been　completely　elucidated.　Here,　we　report　magnetotransport　studies　on　Cr　doped　(Bi1-xSbx)(2)Te-3　topological　insulator　thin　films　grown　by　magnetron　sputtering.　At　the　temperature　of　2　K,　a　giant　negative　MR　reaching　61%　is　observed　at　H　=　2　T.　We　show　that　the　negative　MR　is　closely　related　to　the　position　of　the　Fermi　level,　and　it　reaches　the　maximum　when　the　Fermi　level　is　gated　near　the　charge　neutral　point.　We　attribute　these　results　to　the　Coulomb　potential　due　to　the　random　composition　fluctuations　in　Cr　doped　(Bi1-xSbx)(2)Te-3.　Our　results　provide　a　deeper　insight　into　the　mechanism　of　negative　MR,　and　are　helpful　to　realize　the　quantum　anomalous　Hall　effect　in　the　sputtered　Cr-(Bi1-xSbx)(2)Te-3　thin-film　systems　by　tuning　the　Fermi　level　and　reducing　disorder　effects.