In order to remove a table (with all its content, of course) from your page, select it first and then press the Delete key. Besides the glyph clicking, there is another way to select a table: click anywhere inside it, and then select the <TABLE> from the Tag Selector. The table handlers will show, letting you know that the table is selected.
If you want to only remove a table row or a table column, place the cursor inside it, right-click, and select the needed option from the contextual-menu.