You do can improve the stats, say you have a male rex (60 points on all levels )full of muts 123000/20 on both sides, you can clean 1 side, mate it with a tamed fem get several eggs hatched at the same time and raise the male that carried all the 60 points stats , now you go to the ancestry list and see 1 side has 0/20 and the on the other side 246000/20
Now you get your new male half clean and mate with many low lvl tamed female rexes and let rng do its thing.
The mutation chance is the same even when the female rex is low lvl.
you will at some point get a baby with 01/20 - 246000/20 and one stat=61
If i am wrong about this mutation hunt technique please let me know although this has been proved effective several times in my tribe with several good muts received.
****This is completely different to the technique of getting clean lvls added to increase stats without muts, I really don't even bother with the clean breeding technique.