Does your dual-boot setup use the Grub bootloader from Elementary Linux? That would be the first bit of information needed. If that is the case and you delete its partition, your computer will be unbootable. If you are using the windows bootloader, this won't be a problem.
Since Elementary is an operating system, you don't remove it or delete it the way you would an application you would simply format that partition and then you could install Puppy or whatevr else you want to try. There is no need to delete that partition and no reason to have to do it from windows. To post some more specific information, boot your Elementary and run this command from a terminal: sudo fdisk -l(Lower Case Letter L in the command). It will not make any changes but provide information on your hard drives/partitions to post here for help.
I'm not sure what you mean by your title, GLUG?? did you mean the Grub bootloader?
Last edited by yancek; 08-23-2014 at 08:45 AM.