What's the best way to handle mutual friends after a break-up?
Fighting over Friends
You and your ex likely have enough drama going on between the two of you that you don't need to add, "dividing up our friends" to your list of things to work out. Your friends have likely heard enough about said drama that they won't want to be the subject of any more of it. If you think of your friends as another item to be split up between the two of you, they may not feel valued enough to want to remain friends with either of you. If you think that all of your friendships will remain exactly as they were before, that's not realistic either.
Before you come up with a grand scheme to claim all friends you met through your job or to leave your ex with everyone with whom you started socializing after May 2010, give yourself a chance to recover from the break-up and see who's actually there for you when you need them. An organic order may emerge where you realize who you want to keep as a friend and naturally spend your time with those people. You may notice which mutual friends seem to be popping up in pictures on your ex's facebook wall and think, "Yeah, we were never that close anyway." There is also a theoretical possibility where you don't have to decide, and your friends, mature people that they aspire to be, can remain friends with both of you. If the break-up is so bad that two can't ever be in the same room again, then you have to do some detective work before the next gathering to find out if your ex will be there. If your friends feel as though they have to choose which one of you to invite and you're consistently excluded, then they'll have made the decision for you.
If you and your ex always hung out with other friends as couples, you may have to reinvent your social interactions so that you're not always the odd one out. Start reaching out to other single friends you may not have seen as much during your relationship. Hang out with individual members of those couples or with one couple at a time rather than a whole group. Hopefully your social circle is diverse enough that you haven't been spending all your time with other couples, but if not, consider this a chance to branch out.
As much as possible, you want to avoid badmouthing your ex to your mutual friends, particularly relating to matters that are petty or embarrassing or vindictive. No matter how bad the break-up, if you say mean things consistently, you'll start to come across as a mean person. On the other hand, you need to be able to rely on your friends, and you can work to find ways to discuss your feelings and even vent about your ex's mistakes that won't compromise your integrity or put your friends in difficult circumstances if they do hope to remain friends with both of you.