Q: Truck loses power and tries to stall

I have a 2005 Nissan Titan. About a year ago I was having an issue with the truck losing power, trying to stall and running rough. The truck would run fine for about an hour or two and then would suddenly lose power, would not accelerate, back firing. If I pulled over and let it rest for a few minutes, it would regain power and I could go a short distance till it did it again. If I let the truck rest longer, it would go further before repeating the issue. The CAT light finally came on so I replaced the entire exhaust system. After that, the truck seem to run better but would still act up if I punched the accelerator to pass another vehicle. Now the issues is starting up again and it is getting worst. I was thinking of gutting the CATS but don't know?

My car has 231000 miles.
My car has an automatic transmission.