This answer, which I wrote before I saw the photos, addresses the issue of chipout of the flat tabletop but not about how to cut the top with the side apron if it is still attached to the top.
It may be possible with a circular saw and and a NEW blade with lots of teeth, A 60 tooth finishing-quality blade.
You want the teeth of the blade to plunge into the top veneer, this means you turn the table top over and cut from the bottom side. The bottom of the blade is rotating away from you so as it turns through the table top it is plunging UP into the veneer, this should eliminate chipout on the front end of the cut.
To minimize chipping on the back end of the cut you need to make sure the saw is tracking absolutely straight, this means using a straight edge. (A track saw would be ideal.)
The next best thing would be to make a circular saw straight edge that is sized exactly for your saw. This gives you a solid edge for the your saw to ride against so it does not move side to side.
ALSO use painters tape on the bottom of the cut (the top of the table) for the length of the cut. This will add some insurance against chipping but it is still possible. After you make the cut slowly peel the tape off at a severe angle to the top, not straight up.
You may want to practice on a crappy old piece of table or laminate, maybe from a thrift store or on the free board of craigslist. Watch lots of YouTube for tips.
You still need to deal with the exposed edge left from the cut, There is edge banding or you could use a maple veneer.