I'm planning a home build soon with a 30'x60' ICF basement.  We're going to insulate under the slab with 2"XPS foam as well.  We have a wood stove from a previous home that we will be bringing with us and we want to install it in the basement of the new home.  We'll have a walkout basement so getting wood inside won't be much trouble.  The main floor will be standard wood-frame construction because of cost.

What I have trouble figuring out, is how to install the stove in the basement.  It's a new home so I can build it however I need to, but I can't affect the main-floor of the home.  We know where we'd like to put the stove and there is a bathroom right above, so we would need to put the chimney on the exterior of the home.  I could build a chimney straight to the top of the home and use clay liners, but I don't know how to put that against the exterior of the ICF basement, especially below-grade.  There's waterproofing concerns I'm not sure how we'd handle, and I'm not sure how the chimney would sit against the ICF wall.

We could also try coming up with a stove pipe building a chase on the exterior to run the pipe upwards.  The issues I have with that are centered around the elevation of the exterior grade.  The stove pipe would have to exit above-grade (I'm assuming) and that would put my stove pipe too close to my floor trusses supporting the main floor.  The wall the stove will be close to will not be exposed like the wall with the walk-in door.

I'm open to suggestions.  I'm still doing research on the issue, so if I've made any incorrect assumptions please feel free to let me know.

Surely, you can find a way to keep that chimney inside the building envelope, and save yourself a lot of potential exterior finish, draft, and esthetics problems !
Clay liners would be my last choice, unless they were well insulated to prevent creosote formation. There are proven ways to do that, but the economics are against that option unless an all masonry chimney is essential to complete your overall design.
Most of the newer EPA certified stoves only require a 6" round chimney. Even the older ones are probably not going to be bigger than 8". If you plan to stay in this house for the long term, a class "A " stainless steel insulated chimney in an interior chase would be my choice. For a 6" you would only need a 12" x12", and for an 8" a 14" x14" would work. If necessary 15 degree and 30 degree offsets could be used to get around walls and framing members. If you have a local chimney sweep, you could get an estimate from them. If you get sticker shock, you could just install the chase now and decide later if you really need the wood stove after you have lived there awhile.

I suggest that you abandon this idea and sell the wood stove and do something else like a ventless gas stove or mini split. You didn’t mention if this wood stove has a direct outdoor air vent so you don’t die from carbon monoxide poisoning in a tight ICF house when you run bathroom or kitchen fans. Having penetrations below ground will be a problem later if not sooner.

We started our plans with the chase on the interior of the house and it just didn't work out for us.  We have bedrooms and a bathroom on that end of the house, and the 20"x20" I planned for wasn't fitting anywhere except a closet.  My wife was adamant that we keep all the closet space we could so that option was out.  Putting the chase on the outside of the house is acceptable to me and would add a bit of aesthetics to a relatively simple ranch design.

I have no issues avoiding clay liners.  Good stainless was something I was hoping to use anyways.  Sticker shock also isn't my biggest issue.  I've budgeted enough for a masonry chimney.  If I'm building an exterior chase, I'll be saving a good bit of money on labor.

I'm still not sure how to bring the chimney to the exterior though.  I haven't read anything where someone has brought a chimney through an ICF wall, and I don't want to go high enough to get over the wall.  That puts me in the middle of my floor trusses.

I may have to talk to a chimney sweep in my area with my plans in hand to get the answers I'm looking for.

A couple of things...

First:

By code the air-intake of the wood stove has to be below the fire box, and in most basements the fire box would be below grade. Since the air intake to the basement is above grade the risk of back drafting higher than it would be otherwise, since in a 1-story rancher it cuts the chimney-effect draft pressures roughly by a third to half, depending on the distance below grade vs. the length above grade. That makes it all the more important to keep the chimney fully inside the thermal envelope of the house to enhance the start-up draft. A cold chimney located n the exterior will basically invert the draft direction until the chimney is up to roughly room temperature, which it will be if the chimney is fully inside the thermal envelope of the house. Building a house that's air-tight doesn't help, but it's not the fundamental problem (you can always crack a window or something for starting the stove), it's the distance between the air intake on the stove relative to the lowest air inlet to the house, and the distance from that air inlet to the house and the top of the stack.

Then:

XPS is blown with a combination of HFC blowing agents (the most predominant of which is HFC134a- the same stuff that runs most automotive AC in the US), which are extremely powerful greenhouse gases. Over a few decades as the HFCs leak out the performance drops from R5/inch to about R4.2 /inch, which is the same as EPS of similar density. So for full lifecycle design purposes 2" of XPS is really more like R8.5 than R10. EPS is blown with pentane, with less than 1% the greenhouse potential of HFCs, and most of it leaks out and is recovered at the factory, often burned for process heat. It's only rated R4.2/inch, but it stays R4.2 /inch for many decades. It's also cheaper than XPS per labeled-R, enough so that it's usually cheaper to install 3" ( R12.6) of Type-II EPS (the same stuff most ICFs are made of) than it is to install 2" of XPS. The additional cost of removing the extra inch of dirt to accommodate the additional foam thickness is "in the noise" of the total cost of the slab.

But it's cheaper (and greener) still to use reclaimed roofing foam under the slab. Either EPS or XPS is fine, but do NOT put polyisocyanurate under a slab, since it is slightly hygroscopic and can become waterlogged over time. Most of the foam reclaimers and building materials recyclers are local outfits, but there is at least one that will ship anywhere in the lower 48 (Nationwide Foam). A good place to start looking for used foam is to search the local craigslist for the terms rigid + insulation, eg:

https://chicago.craigslist.org/search/sss?query=rigid+insulation

Used/reclaimed XPS is fine- it's "greener" than virgin stock EPS, since the enviromental hit from the polymer and blowing agents has already been taken. But from a design point of view assume R4.2/inch, no matter how new or old it is.

Here is what I think is one of my finest ideas to keep your chimney inside and keep your wife happy at the same time, or not !

What if you brought that class A stainless pipe up through the floor and through the ceiling somewhere inside the bedroom, without a chase. Build or have built a decorative ornamental iron cage around it ! It could be square or round, with lots of extra ornament. The whole thing could be powder coated in any color you liked. You could have some robe hooks incorporated into the design to use for whatever that might be nice to warmed from the stove heat exhaust. It would be a built in, work of art, heated coat rack. I think all of your wifes' friends will be extremely impressed !

30x60 foundation and there is only one place in the basement it can go. I'm missing something. You will need a clean out for the chimney.