$c = "C:testweb.config"
     $xml = ( Get-Content $c)
     $ConnectionString = $xml.configuration.appSettings.add | Where-Object {$_.Key -eq 'ConnectionString'}
     $xml.configuration.RemoveChild($ConnectionString.ParentNode)
     $xml.save($c)

After removing <appSettings> tag from web.config file. Some special Characters like **&#xA;** are adding to web.config file as below:

<?xml version="1.0"?>
<configuration xmlns="http://schemas.microsoft.com/.NetConfiguration/v2.0">
  <configSections>
    <sectionGroup name="system.web.extensions" type="System.Web.Configuration.SystemWebExtensionsSectionGroup, &#xA;        System.Web.Extensions, Version=3.5.0.0, Culture=neutral, &#xA;        PublicKeyToken=31bf3856ad364e35">
   </configSections>
</configuration>