If you are using the default rwd theme, the footer links are divided into different block.
To check them, open
rwd/default/layout. There you will find two block
cms.xml you will find the block
cms_footer_links. You can remove them as per your requirements.
To remove it from particular CMS page, follow below steps
CMS >> Pages >> CMS PAGE YOU OF YOUR CHOICE
2) Open the design tab and insert below code
<remove name="footer_links" />
<remove name="footer_links2" />
<remove name="cms_footer_links" />
You can remove other elements from the CMS page using the similar technique, you will just have to find the name of the blocks to remove them.