First, decide whether you want to store your image files separately too.
Also, backup everything!
If you currently have these two types of image all mixed together inside your current LR catalog, you need to achieve some way of distinguishing them - doesn't matter how, so long as you can get to a point where you have ALL and ONLY your personal images (or, conversely, your business images) highlighted.
Then with those images selected, you would use "Export as Catalog". This duplicates your current database as it stands at this moment, only selectively - by leaving out all images that have not been highlighted.
There is an important option "include negatives" which if selected, ALSO copies all the image files involved, into a new folder structure inside the destination where you have told LR to put the brand new Catalog. That then refers to these new copied files - LR has separated them out as copies, IOW. Your working Catalog always still refers to the versions of these same files in their old locations (all of this is left untouched by an "Export Catalog" operation).
If "include negatives" is NOT selected, on the other hand, then only database info is copied into the new Catalog location. The image files referred to by this new Catalog are, in that case, the original ones in their current locations - the same as also referred to by your working Catalog.
If you want to leave these (catalog-exported) images showing in your working Catalog you can; or (since they are still highlighted) you have the option to efficiently Delete them.
If you have made separated copies via the "include negatives" option, you can safely Delete from disk the related image files by way of your working catalog. btw LR is clever enough to refuse to delete any physical files which are shared by both highlighted and un-highlighted items inside a given Catalog (via virtual copy).
However if you have not used "include negatives" you will want to only Remove these images from your working Catalog. In that case, the new Catalog is now relying on the continued existence of these files so they must not be deleted from disk.
The end result will be: your working Catalog only has one basic category of image. Your new Catalog has all of the other basic category of image. Personally, I do separate purely business images from personal/general ones this way - while the general advice is often, wisely, "a single Catalog is best" there are counter-arguments in favour of one such, very basic split. I would however, not support finer subdivision (such as by client or even by shoot) - that is IMO far too unwieldy and undermines the whole point of using a database.
hth - RP