Hi rpaccount,
Not quite sure since the title of the thread says removing (deleting) the rows and columns, but the matter in the post is about emptying all the cell values. Below is to clear all cells (not deleting rows and columns).
You can simply copy an empty cell and paste it over a range of cells that need to be cleared.
In below case it is copying an empty cell Z1 of Sheet 1 and pasting to cells ranging from A1 to D50 of Sheet 1.
This clears all the cells from A1 to D50. You can even find the last row containing data and use that data item in the Destination Range.