You CAN cut into a cast iron stack pipe and add a PVC Wye fitting using rubber boots. HOWEVER, you must permanently support the cast iron pipe above the cut because your concerns about the weight are totally valid.
They do make an "official" cast iron pipe support piece that looks like two pieces of extruded aluminum gerts with bends in the middle that surround the pipe. You attach the ends of the gerts to each side of the rafter bay, or floor/ceiling joists, whatever, and then hitch the part around the cast iron pipe tight with bolts.
You can also make a cheaper and just as effective version of this system from a large diameter hose clamp and some metal pipe strap. Install the hose clamp around the cast iron pipe, but don't tighten yet. Cut two strips of metal pipe strap long enough to reach each side of the joist bay you're using for support (be generous!). On each side of the hose clamp, slip in one piece of pipe strap on each side of the cast iron pipe. Tighten down the hose clamp firmly. Bend the hanging ends of the straps upward to form V shapes (it's now wrapped around the hose clamp) and attach each end to the joists/rafters with a couple of screws.
Depending on how much cast iron you are supporting (if you're working in the basement of a 2 story home, it's quite a bit!), you may want to rig up more than one of these pipe clamp gizmos to make sure they'll take the weight.
Now you can cut away the cast iron and the part above where you're working shouldn't fall on your head! I know exactly how much fun this will be for you, and wish you well.
PS: You CAN cut cast iron pipe with a reciprocating saw, but it's a bear. If you can swing the cost of renting a snap chain, I'd strongly recommend it.