Splitting a BSP

I’m trying to split a BSP into two. Until now, the method I used was to guess and check. Is there a smarter/easier way to split a bsp into two?

So pretend I’m trying to measure the distance of the bsp highlighted by the 2 white dots in the image. I want to split that section of the bsp from the original bsp, so I end up with 2 bsp’s. What’s the best way to do this?