In mdb 'cut and paste' is more accurately described as copy and paste. You cannot delete tracks from a playlist by a cut and paste operation. You can only move them within a playlist or copy them to another playlist.
There is a single clipboard that tracks are copied to and from. In contrast to drag and drop cut and paste only copies and moves tracks. Copying from a playlist copies all tracks in the playlist to the clipboard.
To place tracks in the clipboard select them. You can then right click on one of the selected tracks and choose copy selected tracks from the popup menu. Alternatively, after selecting the tracks, you can choose Edit-->copy from the main menu.
Once tracks are in the clipboard you can move or copy them by selecting a single destination track or playlist, right clicking on it an choosing paste/move tracks. Alternatively you can select a single destination and then choose Edit-->paste/move.
Only tracks (not playlists) can be manipulated by copy and paste. However you can copy to the clipboard all the tracks in several playlists. To do this select the playlists and then right click on one them and choose copy tracks from selected. (When tracks are copied in this way they are sorted to avoid duplicates. They will usually be in a different order in their destination then they are where they were copied from.)