Why do you want to do this? Are you trying to shore up the foundation? Is the wall or basement floor cracked or sinking? If so, there is a process called "slab jacking" that is used to correct such conditions. Special equipment and techniques are used to basically inject concrete underneath a building's foundation. It is most assuredly NOT a DIY job.

 

I'm adding a 4' x 6' in-floor hot tub.

Btw - I'm not buying a hottub, because it won't fit through the door. I'm pouring concrete, then covering it with this waterproofing **** for pools.

 

Also, I already dug a 4 foot deep hole in my basement floor, near where this one is going to go, so water level / hydrostatic pressure should me a non-issue (plus I'm on a slope)

 

Interesting. Have you thought this through?? Sounds like you have no idea what you're doing.

 

what is the stone foundation wall supporting? is it supporting floor joists? roof? gable end wall? stop and think about what is holding up the foundation wall right now?

it can be removed, but only after on-site evaluation by someone that knows (either an experienced designer, building or professional engineer).