For some reason under WOT, the turbo seems to sputter and I don't know what it could be. I don't know how to explain it, but under full boost it sounds kind of like pshpshhpshhh.
I bought the car with a catless dp on it, and the owner gave me the stock one to pass smog. After I put the stock one on, it seemed to start doing this. Could it be an exhaust leak?
Possible, but have you ruled out intake charge pipe leaks, vacuum leaks, checked the spark plugs, etc.? A post-turbo exhaust leak shouldn't cause an issue you're describing as far as drivability since the O2 sensor is mounted in the elbow/O2 housing above the downpipe assembly and at WOT the computer isn't even using the stock narrowband O2 sensor.
What is your boost guage reading when you hear it? From what you mentioned I would buy or build a boost leak tester. You can find a how-to to build your own, saves a few bucks and you don't have to wait for it to come in.