OK you obviously know where the files are on the computer, we'll assume here they are in My Documents/Clippings. This means they are all in a sub folder of My Documents in the folder Clippings.

Right click the Start button
click Explore in the pop up and a new window appears - Windows Explorer
On the left side near the top look for My Documents
click the small plus + sign beside it and other folders that are inside that folder now show underneath
click the Clippings folder and all the contents now appear on the right side of your screen.

To select those to delete one at a time simply right click on any file in the right side and in the pop up click Delete. Confirm and it is gone.

To delete more than one at a time hold down the CTRL button on the keyboard then click each item to be deleted so it becomes highlighted. When ready release the CTRL button, right click on any highlighted file and click Delete in the pop up. Confirm.

To delete a contiguous batch click the first one to be deleted to highlight it, hold down the Shift key and click the last one to be selected. Now all those in between are highlighted, right click on any one of those and click Delete in the pop up. Confirm.

Done, assuming that is what you want.

I believe poster is talking about the "Gardenweb" clippings. Click on the clipping you want to delete. Scroll to the bottom of the page and you will see the option to delete the clipping.