I just tested all of these and they worked as expected. I added them to the Layout Update XML section of the CMS page I wanted them removed from, and then cleared the Magento cache.

<reference name="head">
    <!-- For a JS in the js folder -->
    <action method="removeItem"><type>js</type><name>directory/file.js</name></action>
    <!-- For a JS in the skin folder -->
    <action method="removeItem"><type>skin_js</type><name>functions.js</name></action>
    <!-- For CSS in the skin folder -->
    <action method="removeItem"><type>skin_css</type><name>css/local.css</name></action>
    <!-- For CSS in the js folder -->
    <action method="removeItem"><type>js_css</type><name>local.css</name></action>
</reference>

Credit to @Shadowbob - https://stackoverflow.com/a/19662670

Remove the layout tags.

<layout><\layout>

I just tested all of these and they worked as expected. I added them to the Layout Update XML section of the CMS page I wanted them removed from, and then cleared the Magento cache.

<reference name="head">
    <!-- For a JS in the js folder -->
    <action method="removeItem"><type>js</type><name>directory/file.js</name></action>
    <!-- For a JS in the skin folder -->
    <action method="removeItem"><type>skin_js</type><name>functions.js</name></action>
    <!-- For CSS in the skin folder -->
    <action method="removeItem"><type>skin_css</type><name>css/local.css</name></action>
    <!-- For CSS in the js folder -->
    <action method="removeItem"><type>js_css</type><name>local.css</name></action>
</reference>

Credit to @Shadowbob - https://stackoverflow.com/a/19662670