Is it possible to abstain from blame?

You can abstain from blaming someone, but you can't abstain from blame if someone else blames you. This is because you can only abstain from things that you might do or enjoy, From NOAD:

abstain |abˈstān| verb [ intrans. ] 1 restrain oneself from doing or enjoying something : abstaining from chocolate.

What you can do is reject such blame, or fail to accept or acknowledge it.

I don't know if I am stretching the meaning too far, but when Pontius Pilate washed his hands (according to the Bible) he was, in a sense, abstaining from the blame for Jesus Christ's crucifixion.