Orders cannot be deleted* but empty and/or $0 orders can be hidden.
Empty orders (all items returned, all payments refunded) are automatically hidden from your Order page, but remain accessible for viewing via the Advanced Search tool.
$0 orders (containing only complimentary tickets/items) will display on the order page unless you choose to hide them.
*Maintaining a "paper trail" of all transactions is a fundamental principal of accounting best practices because it allows one to trace any sequence of events that transpired.
To hide a test order
Go to Orders > click on Manage link of desired order: