You should definitely NOT tag the images while you are looking at them on the card in the card reader. If you want to keep secure copies of your images, you could ingest them to your main drive and a backup drive at the same time (That's a feature of Photo Mechanic) That would be much, much safer than keeping some on the card and deleting some. When you delete partial contents of a memory card and then shoot more images to that card, you risk corrupting the card. It's a very, very, very small risk, but it does happen. It is by far safest to shoot, ingest and edit on your main drive, backup someplace safe, then format the card and start fresh each time.
Mick