sample.xml

<file>
  <categories>
    <category>cat1</category>
    <category>cat2</category>
    <category>removecategory</category>
    <category>keepthisone</category>
    <category>deletethisone</category>
    <category>somethingelse</category>
  </categories>
  <otherstuff></otherstuff>
</file>

I'm not so good with Powershell but "it worked on my computer" :)
The node with the text "somethingelse" in it has been deleted.

Get-ChildItem sample.xml | % {
    [Xml]$xml = Get-Content $_.FullName

    $xml | Select-Xml -XPath '//category' | % {
        if ($_.InnerXml -eq 'somethingelse') { 
            $_.ParentNode.RemoveChild($_) 
        }
    }

    # $xml.OuterXml | Out-File $_.FullName
    echo $xml.OuterXml
}