In this post I use an asterix, *, to show when an example is ungrammatical.
*Killing people is not a crime you can commit and get away. (ungrammatical)
Killing people is not a crime you can commit and get away with.
The preposition away cannot take noun phrases as Complements:
However, it can take preposition phrases as Complements:
- Get away with the crime
- Get away from here
The original poster's examples have a noun phrase, which contains a relative clause:
- *a crime [you can get away ___ ]
- a crime [you can get away with ___ ]
This relative clause has a gap in it, shown by the ___ in the examples above. We interpret this gap through the antecedent string a crime. We can model the noun phrase like this:
- *a crime [you can get away (a crime)]
- a crime [you an get away with (a crime)]
We can see that the first noun phrase here is ungrammatical because the gap representing a crime is occurring as the Complement of away. We have already seen that away cannot take noun phrases as Complements. The second noun phrase is grammatical because the gap representing a crime is occurring as the complement of the preposition with. The preposition with can take noun phrase Complements. Notice that in this example the preposition phrase beginning with the word with is occurring as the Complement of the preposition away.
With regard to crime related vocabulary, the idiom get away means something similar to escape. The idiom get away with something means to do that thing but not get caught or not get punished. The Original Poster needs the second meaning here. You cannot kill people and not get caught and not get punished. (Or at least that's what the sentence says!)