If you want to delete a horizontal slice from the image and move up the lower part of the image (that is under the removed slice), you don't really need to delete that slice at all.
Simply select Select tool (press S) then select that "lower" part from the image you want to retain and be moved up, then change to Move tool (V) and move the selection up with Ctrl+Up, the selected (and moved) image part will cover the "slice".
You can move the selected part with the mouse but that is unstable as you cannot lock the movement to only Y axis.
Finally crop the image to the proper size.
This will also work if the would-be-deleted slice is on the edge of the picture, although a single canvas resize will do the same.