I use File Manager HD and don't have any issues seeing my sdcard and to cut and paste I just long press on the file and select cut then move to the location I want it copied to and hit copy.
i use X-plore as a file manager and it works great as it has duel panels to move a file kust press and hold then a menue comes up giving you options of copy past cut move ect i tried several different versions and found x-plore the best for me much better than the stock file manager