I'd recommend breaking this into three tasks to see if this will work for your site and your users. As
@Optic and
@Martok have pointed out, going down the route you're proposing splits your user base, their ability to easily communicate with one another (and impossible if people decide not to use both sites), and will cost you more in license fees.
As a first task I'd create a new category node and sub-forum nodes off the root and make a logical split by moving the relevant posts and threads into those new nodes. Even if in the end you decide this is all you do, then your site is better organised.
If you decide to then continue, create two new sets of user groups to replace registered users and mod groups (and any others you may have). You can then send out messages to ask users which set of groups (or both) they want to be in. At this point it shouldn't restrict access if they're not in the relevant groups for "the other side" but it will at least give you an idea of where people are at. This is a large undertaking but will really help you understand your users. If you have some good mods you could ask them to help contact your users to ask them the question and give them the choices.
With a small amount of interrogation of the underlying database, you can then run a few queries to see if people in groups on either side only are posting in forums on the other side, or messaging people with groups on the other side only. This analysis is important because it's the best way to show if users are truly using the site for both topics or communicating with your whole community whilst only identifying themselves with one side of the community. If that's happening and you forge forward with the split you could seriously damage both of the emerging sites. Some people may leave forever, and even if you try to reverse the split it may be too late for some.
If the analysis shows it's not good to make the split, then treat it like a bullet dodged and your site is still split into the separate categories so organised better.
Even if you don't do the full split, you can still change to a more relevant domain name encompassing both sides of the community if you want, and you'll have focused categories for your content.
If the analysis shows that you could split the community without negatively affecting your users usage of your community then having already re-organised it upfront, you can create a backup and restore to the new domain / site and just get rid of the relevant categories and sub-forums on each side.