バッチファイル内でPowerShell を使ってファイルをゴミ箱に移動するには、

powershell.exe -Command "Clear-RecycleBin -Force -ErrorAction SilentlyContinue"

set destination=Y:\temp
for %%f in (%destination%\*.png) do (
    echo %%f ToRecycleBin 
    powershell.exe -Command "Add-Type -AssemblyName Microsoft.VisualBasic; [Microsoft.VisualBasic.FileIO.FileSystem]::DeleteFile('%%f', 'OnlyErrorDialogs', 'SendToRecycleBin')"
)
timeout 11

set target=Y:\temp
for /d %%f in ("%target%\*") do (
    echo %%f ToRecycleBin 
    powershell.exe -Command "Add-Type -AssemblyName Microsoft.VisualBasic; [Microsoft.VisualBasic.FileIO.FileSystem]::DeleteDirectory('%%f', 'OnlyErrorDialogs', 'SendToRecycleBin')"
)
timeout 11