My guess is out of spec bases, and or bad drill job and or bad rings.
The rings are probably way out of alignment and if not aligned you could be torquing the scope when you tighten the rings.
It happens.

All the package bases and rings are garbage IMO and you could not give me a 2 piece set of bases anyway unless thats the only option.

Best = Farrel one piece base and a good set of steel rings.
Second = EGW or equal alum base and a good set of rings, burris etc.

Mount the base and rings, crank the base of the rings down, check them with a Wheeler alignment kit then hone them, until they are perfect, then you will have rings that are aligned.

If the base screw holes in the action are off then you need to bore sight it and check base alignment.

I had a rifle (not a savage) that was so far off I had to put a 1/32" brass shim on the right side of the
front base just to get it back close to zero.

I did however have a flat back Savage that the holes were a bit off, but the flat back part was also angled. Had to bed the base.

If the holes are mis-drilled you can improve it with a shim as above. Burris signature rings, etc.

To do a general check, get your hands on a new non adjusted scope that is factory zeroed, mount it loosely, put in a rest of some sort, pull the bolt and look down the barrel and compare to the cross hairs.

That will give you a rough idea.