Q:

Need to remove permission level from a SharePoint group using PowerShell

I was able to create a PowerShell script that creates a new permission level and assigns it to a group. However, I noticed that it doesn't replace the previous permission level of that group. So how can I create a script that removes the additional permission level of that group. 

A:

I found a script on the MSDN SharePoint forum that seems to have the answer.  What I get from looking at the script is that it seems you have to remove the role definition for that permission level from the role definition bindings on the role assignments for the group.  (Say that three times fast! ;)
Directly pulled from the link above:
function Remove-SPGroupPermission([Microsoft.SharePoint.SPGroup]$group, [string[]]$permissions) {
  $ra = $group.ParentWeb.RoleAssignments.GetAssignmentByPrincipal($group)
  foreach ($permission in $permissions) {
    $rd = $group.ParentWeb.RoleDefinitions[$permission]
    $ra.RoleDefinitionBindings.Remove($rd)
  }
  $ra.Update()
  $group.Update()
}

EDIT:
Ok, so what you want would probably look something like this, in a very simple form:
$web = get-spweb http://url/to/your/web
$group = $web.SiteGroups["Owners"]
$ra = $group.ParentWeb.RoleAssignments.GetAssignmentByPrincipal($group)
$rd = $group.ParentWeb.RoleDefinitions["Full Control"]
$ra.RoleDefinitionBindings.Remove($rd)
$ra.Update()
$group.Update()
$web.Dispose()

Or, if you wanted to use the function posted above, something like this:
function Remove-SPGroupPermission([Microsoft.SharePoint.SPGroup]$group, [string[]]$permissions) {
  $ra = $group.ParentWeb.RoleAssignments.GetAssignmentByPrincipal($group)
  foreach ($permission in $permissions) {
    $rd = $group.ParentWeb.RoleDefinitions[$permission]
    $ra.RoleDefinitionBindings.Remove($rd)
  }
  $ra.Update()
  $group.Update()
}

$web = get-spweb http://url/to/your/web
$group = $web.SiteGroups["Owners"]
$permissionsToRemove = @("Full Control")

Remove-SPGroupPermission -group $group -permissions $permissionsToRemove

$web.Dispose()

