Can I mix oxycodone and codeine safely?

No, it is not a safe combination, there is a major interaction when taking both.

Interactions between your drugs
Major
codeine oxyCODONE
Applies to: Tylenol with Codeine #3 (acetaminophen / codeine), oxycodone

Using narcotic pain or cough medications together with other medications that also cause central nervous system depression can lead to serious side effects including respiratory distress, coma, and even death. Talk to your doctor if you have any questions or concerns. Your doctor may be able to prescribe alternatives that do not interact, or you may need a dose adjustment or more frequent monitoring to safely use both medications. Do not drink alcohol or self-medicate with these medications without your doctor's approval, and do not exceed the doses or frequency and duration of use prescribed by your doctor. Also, you should avoid driving or operating hazardous machinery until you know how these medications affect you. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor..

https://www.drugs.com/interactions-check.php?drug_list=1770-0,48-8460

Do consult with your Dr..