Social Sound Design has been a great resource to me over the years and I've gained a lot of knowledge from all of the people contributing. And in an effort to keep that momentum going I choose to post an answer to this question - with reservations.
I do not like the title of this question. Nor do I like the grotesque escalation of violence in every form of media, especially lately in light of the latest round of mass killings in America (most notably the murder of a classroom full of kindergarten age children), it makes me sick to my stomach to think that watching people die on screen is considered "entertainment". To be called upon by directors and producers to create the sounds of torture porn, murder and death for people to sit and watch strikes me as - absolutely wrong. But hey, who am I to argue? The public eats this crap up like biscuits and gravy.
All that being said, I will offer up this piece of creative sound design advice, had I been put in your position of needing to create it: A chainsaw cutting through most any object will have a strain put on its motor, causing it to "bog down" temporarily. If you construct the chainsaw engine with this in mind you will probably lead the audience to think that the saw is really working hard to cut its way through. And people will most likely love that and tell all their friends how gross it was, and we will all continue to become desensitized to the violence around us.