A cutting tool was a tool which could cut through something.
Maitland used an electromagnetic cutting tool to get through a door on his ship. (TV: The Sensorites)
Luke Smith noted that he would need a cutting tool to shut down a Slitheen transducer safely. Sarah Jane Smith's sonic lipstick served this purpose. (TV: Revenge of the Slitheen)
The Daleks used a hot iron manipulator arm, the cutting arm, to cut through metal. (TV: The Daleks) On Spiridon, they used one to cut through a thick door. (TV: Planet of the Daleks) In an alternate timeline in which they invaded Urbinia, one Dalek suggested using a cutting flame to breach the spaceport hangar bay in Kiria City, but another decided they would use hostages instead. (AUDIO: Daughter of the Gods)