If you cut your bedsides the back of the bed will come apart. There is support structure in there that is spot welded together, as well as some triangular type strap bracing that runs upwards. That is precisely why I didn't cut my box when I built my bumper. Also becauise it wouldn't be worth the time. The whole bed is going away.
If you want to build a race truck, build a race truck. If you want to build something "inspired by", do that too. To each his own. But keep it functional if it's a daily driver. It already looks like you can't use your bed because your tailgate moves very little. If you had gone with a swing open design you would have been better off.
Here's my truck, perhaps you've seen it before: