Question

If diamond is a good conductor of heat then why is it used for cutting and drilling purposes.If I use some bad conductor of heat there is no way the tip gets overheated.

Answer 1

Besides being a good conductor of heat, diamond is the hardest natural material. It is therefore used as an abrasive for cutting other substances.
As mentoned by Sharath k Menon, diamond is present at the tip of the cutter and due to its high melting point there would not be a detrimental effect on heating.