Are hiccups a side effect of oxycodone?

No side effects per say but you'll feel the withdrawals if you don't stop taking it by reducing your dosage incrementally. Unless you like withdrawals.

Easiest way to reduce your level is to cut your pill into quarters or halves, then reduce it by 1/4 or 1/2 (depending on how much withdrawal symptoms you have afterward) each week or 2 weeks, and keep dropping it by the same amount until you can stop.

If you try and stop cold turkey you're in for a rough time - it's not recommended.