There is a property flag that controls whether or not rows/columns can be appended during a paste.
//C#
this.gridControl1.CutPaste.ClipboardFlags |=
(GridDragDropFlags.NoAppendCols |
GridDragDropFlags.NoAppendRows);
''VB.NET
Me.GridControl1.Model.CutPaste.ClipboardFlags = Me.GridControl1.Model.CutPaste.ClipboardFlags _
Or GridDragDropFlags.NoAppendRows _
Or GridDragDropFlags.NoAppendCols