I separated the chra from the exhaust housing by using a bolt with a nut and socket to pry against the two housings. Similar to what Samnavy did. However in my frustration I left the compressor housing on and now my snap ring inside is stuck on one side and I cannot remove it. Any suggestions?

 

Screwdrivers and/or picks work well, just squeeze until you can work the tip between the housing and snap ring, then work it around until it pops out of its channel.

 

I'd suggest serious clean up around the snap ring, You need a blow tip and compressed air to assist.
I'd try to get all the paint (?) clear of the snap ring
Then soak it in your favorite penetrating oil. I like "pimp juice" (1/2 ATF and Acetone) but anything will help.
Get the snap ring to rotate in it's groove first then try for removal.
Cleaning and lubricating is 1/2 the battle...

Prying them with picks and screwdrivers sometimes damages the ring/groove and I try to avoid that.
A final " I'm going to remove this even if it kills stuff" is to hook one side on the ring through the hole (ice pick, large 90 degree pick)and peel it out.
This will destroy the snap ring but usually saves the groove...

 

Another suggestion is to heat the turbo up. 10 min at your ovens lowest temp will do fine.
Aluminum expands more than steel and sometimes running it up to 200 degrees helps.
Use a disposable pan (turkey pans work great) to catch any drips.
Welding gloves (oven mitts) help with dealing with the 200+ degree parts.

This will anger any females you live with so do it when they are not around....
It will make the house stink.
If you wiped out her oven mitts buy new ones FAST!

 

And then try to remove the clip when it's hot?

 

Yep, letting it cool defeats the aluminum expands more when hot thing...

I'd try the cleaning and lubricating thing first. That PB Blaster will work great.
The real trick is to get the snap ring to rotate in its groove. Once it finally moves you will have it whipped...