Yes, you can! Though the photos will still exist on your camera and on the web portal.
The photos taken by your camera are saved to the SD card in the camera unless you have Overwrite turned on - when the SD card is full, Overwrite will save any new photos over older files on the SD card.
Photos sent by the camera will still be available on the web portal for 30 days, after which point they will be purged. However, if you prefer, you can go to the web portal to delete them manually.