Selecting cells and pressing Delete just deletes the contents (i.e. text, graphics etc.) of the cells, not the cells themselves. The only exception to this is when you select the entire table. If you do this and press Delete it will delete both the contents and the entire table!
1.Select the cells whose contents you want to delete. (Don't select the entire table as this will delete both the contents and the entire table.)
2.Press the Delete key.
This is only possible with entire rows and columns.
1.Select the cells, rows or columns you want to delete.
2.Select the Delete tool in the Table tab and choose Rows or Columns to delete all the cells and their contents.
Table Properties (Reference)
How table sizing works (Reference)