Got a mild turbo car making 240ish rwhp. Has a 2.5 exhaust with a failed muffler, so its stupid loud.
can get a very cheap mazdaspeed axle back wich measusures 2.25.

Will this kill any power?

 

Yes

And spool

 

You will loose a bit of power, but not a lot, and you might like what it does for you in terms of controlling target boost.
I went from a 2.5 inch down pipe connected to the stock exhaust from cat back, to a 2.5 inch downpipe connected to a 3 inch cat back with a resonator and street-ish exhaust. (actually no cat in either case)
Now I have a bit of boost creep, up 2 lbs, which certainly means more power. Although the creep does not always happen. This is a bigger change than you are thinking about (though in the opposite direction).
I thought the car was great before switching to the 3 inch cat back.

The more restrictive exhaust means the waste gate can more easily achieve its intended target boost.
More free flowing means better spool, but the waste gate has to get bigger and better to maintain target control.