This
feature is found in Settings > Store Settings > SMS Settings. The
found number placed in the may not be entered correctly. Numbers should
include a + and your country code (For example: +61XXXXXXX). If you
don't have this set up, the SMS's are being sent but is not likely
received by the customer.
If you don't want to receive the order SMS's can either remove the tick in "New Order Alert (will be sent to store manager)".