When you use Select-Object and give it just one property name, you get and object with just one property. But even though it only has one property, you still have to reference that one property by name:
Add-PSSnapin Microsoft.Exchange.Management.PowerShell.E2010
. $env:ExchangeInstallPath\bin\RemoteExchange.ps1
Connect-ExchangeServer -auto
$PU = Read-Host "Enter Username"
$did = get-activesyncdevice -mailbox $PU | Select-Object identity
Remove-ActiveSyncDevice -Identity $did.identity