Remove child block by layout update or programmatically

By using layout update:

<reference name="left">
     <reference name="enterprisesearch.leftnav">
           <action method="unsetChild"><alias>category_filter</alias></action>
     </reference>
</reference>

Programmatically:

$this->getLayout()->getBlock('enterprisesearch.leftnav')->unsetChild('category_filter');