If memory serves me correctly
The Mini-14 takes down like the M-14 rifle. After removing the magazine and pulling the bolt back to ensure that it is not loaded:
1) Let the bolt forward.
2) pull down on the trigger guard. It pivots forward toward the muzzle. Now pull the trigger guard out.
3) Turn the gun upside down. You may lift the stock off the barreled action.
4) Remove the slide (operating rod) spring and its guide.
5) Remove the slide (operating rod)
6) Remove the bolt.
Examine the bolt and pay particular attention to the firing pin. If you push on the firing pin's tail, does it project through the firing pin hole? If you pull back on the firing pin tail, does the firing pin withdraw from the firing pin hole?
If the firing pin is fine, see how freely it moves within the bolt. If it's sluggish, the firing pin channel must be cleaned.
If the problem cannot be attributed to the firing pin, it may be the bolt not locking up. Check the channel and the areas where the bolt locks up. Make sure it's clean. Oil the bolt lugs.
Also clean the track way the slide travels along. Lubricate it.
Also clean the slide (op rod) spring, spring guide and the channel (the hole where the slide and spring guide fits in).
Finally, soak the gas piston and blow it out with a compressor. Make sure air flows freely through it.
Vigilantibus et non dormientibus jura subveniunt. Molon Labe!