Hey rama! This Yahoo! blurb fails to follow Mr. Rewrite's First Rule of Who/Whom: If ever one feels like using whom, simply write around the problem or risk the wrath of mean-spirited and-or wannabe grammarians who live for the opportunity to savage writers over who/whom errors. Rewriting also helps because whom usually suggests that a passage is far from conversational. William Safire, as quoted by Bryan A. Garner in Garner's Modern American Usage, put it this way: "When whom is correct, recast the sentence."
In this case, the blurb would read better by getting rid of the unnecessary comma and the perceived need for whom or some substitute that would apply more elegantly to the word group:
The mayor calls out a group he blames for an eruption of violence in Chicago.
Or one could say:
The mayor calls out a group that he blames for an eruption of violence in Chicago.
Whatever the decision, who/whom only apply to human beings and not to entities created by human beings. In this case, the blurb is referring to gangs. While he would disagree, Mr. Rewrite supposes one could argue that whom applies because gangs consist of human beings. But the sentence reads horribly with whom. So eliminate it or write around it to keep the sentence conversational.