While I think working from a SD card is not optimal, that’s your choice.
- Can darktable write to the SD card at all? That is, if you edit an image, do you get the corresponding XMP file on the card? If you export, does darktable create the output directory, and the output file? Performing those tests would tell us if it’s a general problem writing the card, or if it is related to deleting.
- Can you write to the card from other apps? E.g. save a file from Notepad? Can you delete files from Explorer? (Ah OK, I just saw the native filemanager seemingly has this ability in one of your comments above.)