。
He committed murder for the sake of his ambition.
Literal
Ambition [for-のために] he [topic-は] murder [obj-を] committed.
~のために here is the purpose/beneficiary sense 'for the sake of, in order to' — distinct from the causal 'because of' sense (context and syntax disambiguate). 殺人を犯す is the set collocation for 'commit murder'; 犯す is the verb specifically used for committing crimes/offenses.