SKSs and Mini-30s have been used for many hunts in my family.
You do generally fall below the ".30-30 power level" in a 7.62x39mm auto-loader, but choosing a good bullet can make up for the loss of velocity (and, of course, the rifle needs to be accurate enough to do the job).
One of my family's favorite choices for Elk is the old surplus ammo that was converted to "hunting ammo" by grinding the tip of the FMJ, but they still have a steel penetrator inside. The jacket fragments upon entry. The lead core and steel core separate. The lead core generally tumbles, and veers of to an unpredictable location. But the steel core blows through everything in its path. Even an animal the size of an Elk has never needed more than 2 quick shots with that "Hunting" ammo. Hit them in the ribs, with the intent of sending the penetrator through the heart, and they're done.
You're unlikely to find any of that 'converted' ammunition, though. I haven't seen any for sale in at least 10 years.
A more standard choice for penetration is the Barnes TSX or TTSX.
For standard performance, Wolf 154gr SP, Prvi Partizan 123gr RNSP (the round nose doesn't cause feeding issues in an SKS), Remington 125gr PSP, and the Winchester123gr load all get good reviews.
