$item = Get-Item -Path "master:\media library\images\koala"
$itemNew = Get-Item -Path "master:\media library\images\penguins"
$links = Get-ItemReferrer -Item $item -ItemLink
foreach($link in $links) {
    $linkedItem = Get-Item -Path master:\ -ID $link.SourceItemID 
    $itemField = $linkedItem.Fields[$link.SourceFieldID]
    $field = [Sitecore.Data.Fields.FieldTypeManager]::GetField($itemField)
​
    $linkedItem.Editing.BeginEdit()
    $field.Relink($link, $itemNew)
    $linkedItem.Editing.EndEdit() | Out-Null
}

# Crafted by Dylan
​
function Remove-ItemLink {
    param([Item]$item)
​
    $linkDb = [Sitecore.Globals]::LinkDatabase
​
    $links = Get-ItemReferrer -Item $item -ItemLink
​
    foreach($link in $links) {
        $linkedItem = Get-Item -Path master:\ -ID $link.SourceItemID 
        $itemField = $linkedItem.Fields[$link.SourceFieldID]
        $field = [Sitecore.Data.Fields.FieldTypeManager]::GetField($itemField)
​
        $linkedItem.Editing.BeginEdit()
        $field.RemoveLink($link)
        $linkedItem.Editing.EndEdit()
    }
}
​
# Example usage: delete items along with their references that have passed a certain date defined by a 'date' field
$today = Get-Date
$todayIsoDate = [Sitecore.DateUtil]::ToIsoDate($today)
$query = "/sitecore/system/Modules/Mysite/Service Schedules/*[@date < '$($todayIsoDate)']"
$itemsToDelete = Get-Item -Path master: -Query $query
​
foreach($item in $itemsToDelete) {
    Write-Host "Cleaning up $($itemsToDelete.Paths.Path)"
    Remove-ItemLink -Item $item
    Remove-Item -Path $item.Paths.Path
}