A pressure washer should cut through many kinds of foam especially if you use a 0° turbo nozzle. This is a nozzle that shoots a very narrow stream of water while oscillating in a circular pattern. The chance of success increases with PSI of the pressure washer -- a gas-powered washer will be more likely to eat through the foam than a small electric washer will be.
However, a consumer pressure washer is quite unlikely to cut through the wall of a corrugated HDPE drain pipe. (Pressure washers/pumps of similar spec are used in hydroexcavation, which is an industry-standard practice for uncovering buried utilities without risking damage to them!)
It should be easy enough to stay clear of the to-be-abandoned pipe while installing a new pipe simply by staying far enough to the side of the old one. There could be an issue of your tunnel running into the slab-jacking foam material though. Clearly the foam is going to be filling voids directly below the slab -- and your drain pipe is likely to be shallow, occupying that same vertical region. All you can do is try though.
What have you tried so far for clearing the foam blockage from the existing pipe? If the pipe is nearly straight, and assuming that it is not collapsed, you might be able to clear or at least penetrate the foam blockage from within it by mechanical means. The latter two in this list would be capable of damaging the existing pipe, but using them to intentionally damage or remove portions of it would be arduous.
- pressure washer inserted from either or both ends
- a long drill bit ("bellhanger" or "flex auger" drill or similar, especially in combination with something homemade functionally similar to the Rack-A-Tiers Bumper Ball product)
- a valve key (or "curb key") driven in with a hammer, then twisted, might take little bites out of the foam