See my attached file.
Firstly turn your pipes into solids. As per my layer 01
Then copy all pipes to a second layer due to parts falling away when doing boolean diff operation.
Now go back to layer 01 and select boolean difference tool. When asked to select first set of polysurfaces, select the red ones and right click ("enter"). Now select the blue surfaces as the secondary set as prompted by boolean diff tool. Then right click (enter) and the blue pipes will disappear and the red pipes will be cut. Delete the waste parts and you now have your profile.
Repeat the procedure with the spare set as in layer 02, but select the opposite pipes when doing the boolean diff.
You can now select one of each resulting cut pipes and "explode" them. The outer skin surface can now be unrolled and the resulting unfolding can be used to cut the profile on a rotary plasma cutting machine.
This works very well and I use it daily for profiling pipes to manufacture typical water pipe sections.
There are some very important small issues to fix on the resulting unfolded profile to compensate for pipe thickness as well as the fact that plasma / laser / waterjet cutting in a simple 2.5D configuration will always cut a mitre due to the line from outer surface to the centreline of the pipe.
Feel free to ask me to clarify some issues if needed.