Is it safe to mix oxycodone and ibuprofen for pain relief?

Safety. Yes it is ok. But remember always consult with the prescribing physician.
Yes. Oxycodone is a powerful opioid, and it can be mixed with and NSAID (anti-inflammatory). One should be cautious with use nsaids on a long term basis irrespective of mixing them with other medications. Some heart patients should not nsaids at all. The physician can make the decision on case by case basis.