As you know that how to create links for text, image, email link, on page link on a site page, direct compose link in Create links on Google Sites page. Now if you want to remove any link from you site page, you can simply remove it.
In edit page mode, point your cursor on the text, image email etc link and after a regular click, you will see the option pop up with a link, simply click on the Remove and the link will be removed.
Remove text base links, option menu should look like this:
Remove image base link, option menu should look like this:
Note: The cross under the red mark is to remove the image, not to remove the link.