The question here is attacking a mixed stack with enough defensive Catapults in order to weaken Pikemen enough to render the stack completely useless by then attacking it with enough Knights.
Personally I think it's kinda weird to be doing that. If the stack only has two Pikemen, your best course of action is to use Shock Knights to attack the stack. Your Knights may or may not die (they have retreat odds, too), but they WILL draw the Pikemen up to defend and they WILL most likely weaken them to the point where they'll be susceptible to further Knight attack.
The next unit that'll probably be up for stack defense are the Knights themselves, and in that case, it'll be nice to have Formation Knights or even better, Shock Elephants to draw up the Knights up the defensive priority in order to kill them at best odds.
At that point, the stack will have little to no stack defense (since it's carrying an abnormal amount of CR units) and it'll be trivial to mop it up with Knights or whatever. Past a certain point, the siege will die en masse, but really, once the stack defenses are done, the stack is more a walking pile of XP than a real threat.
I find that messing with a stack's defense priority is a more cost-effective manner of killing it than sacrificing large numbers of siege units. The only time the reverse is true is when you're up against a unit that can't be defeated using defense manipulation, such as a Protective Fortified Longbow on a hill, at which point it's best to just level the best CR siege against it and hope the collateral damages enough of its buddies to render defense manipulation viable again.