Deleting images using your computer have the potential of causing problems with the card. The recommended method is to format the card with the camera after you have downloaded the images.
Lightroom is designed to never touch the items on a memory card - only to read them. I would be shocked if it would let you delete them.
You need to delete them via the computer's OS or the Camera's onboard functionality.
I am working on Adobe Lightroom and am importing RAW files from an SDXC card on a Windows 10 machine. However, after import and reworking the pics I get rid of some by removing them from disc (right click to get to menu; the remove from disc). However, it won't remove the files from the card but just will creates copies in the bin but keeps the originals on the SDXC card. Even emptying trash will not solve this issue. Files are still there.
Are there any suggestions how to resolve this?
I think you're a little confused. When you use LR to import images from a memory card it COPIES those images off the card to a folder of your choosing on your hard drive. Then when you edit some and delete others it is deleting them from the folder on your hard drive they were copied to on import. Which would leave all images on the card. To remove images from a memory card put that card back in the camera, go into the menu system of the camera and Format the card.