There's a useful idiom here: 'Two wrongs don't make a right.'
Incidentally, the etymology of 'atone' is interesting: Online Etymology Dictionary : only a miscreant can atone - and become 'at one' with the wronged party; so a state obviously can't do it.
b
Perhaps, we could say
One ought not exact vengeance for a crime by committing another.
Could we possibly say
You cannot redeem a crime by committing another.
?
'Redeem' doesn't work for me. Don't you redeem a person from a thing?
b
I found this online:
Guza's idea of criminal redemption obviously is to redeem a crime with a crime. Of course I could hear the spin machine now trying to write this away as they do everything by suggesting they are "showing the complexities and consequences of violence."
Does the word "redeem" have that kind of meaning?
To me it seems to mean righting the/a wrong by committing another wrong.
That was my first thought, but I was reminded by the OALD of this: "redeem [...] to make sb/sth less bad SYN COMPENSATE FOR: the excellent acting wasn't enough to redeem a weak plot. ⋄ The only redeeming feature of the job [...] is the salary."
I don't, however, think you can redeem a crime.
Context is always important; labelling is rarely important.
I felt pretty sure at the time of writing that my person/thing thought was an over-simplification! The 'compensate for' definition is unarguably right. It's often used for contrasting features or things: 'the interminable boredom was redeemed by....' or 'her mischievousness was redeemed by a rueful and apologetic grin that made it impossible to stay angry for long'.
Incidentally 'redeeming feature/s' account for more than half BNC hits for 'redeeming =+ <noun>': 38 out of 67. So if you hear/see 'redeeming' it's a better than even chance that the next word will be 'feature/s' (if you're in a British English context. In COCA, 'redeeming feature/s' is quite common, but not nearly as common: 'Feature' comes 4th and 'features' 6th, with their combined totals amounting to less than the total for the leading COCA phrase - 'redeeming qualities'.)
More here British National Corpus (BYU-BNC)
b
Perhaps:
"You cannot remediate a crime by committing another one."
or
"You cannot ameliorate [the effects of] a crime by committing another one."
?