A bend is the part of the run where the shape is doing work. Cut through it and the two halves have nothing to register against each other: the curve that was continuous becomes two arcs that must be lined up by eye, and the joint has to hold a direction the material was previously holding for you.
There is a practical problem too. A cut on a curve has a face that is perpendicular to nothing convenient, so the saw follows the surface and the resulting edge wanders. Squaring it afterwards means removing material from a place where there is very little to spare.
The first thing lost is length, which is expected. The second is the smooth transition the bend provided, and on a system built around a continuous curve, a joint in the middle of it becomes an interruption in both the flow and the appearance.
The third thing lost is tolerance. A straight joint that is slightly out of square can be pulled straight by the clamps on either side. A joint on a bend has no such forgiveness, and a small error in rotation becomes a large error at the end of the run.
Wherever there is room, take the cut off the bend and onto the straight leg on one side of it. The length changes slightly, which usually matters less than the quality of the joint, and the joint gains a face that can be measured and a run that can be aligned.
If moving the cut means removing more material than intended, make up the difference with a short insert on the straight rather than with a longer cut through the curve. Two joints on straights will outlast one joint on a bend, and both are far easier to make properly.
Some systems have no straight section within reach: a tight downpipe, a short link pipe between two components, an engine bay where every tube is curved. Then the cut has to fall on the bend, and the approach changes from avoidance to control.
Mark the rotation before cutting, with a line across the bend that will still be visible on both halves afterwards. That line is the only thing that will let you put the two arcs back in the same plane, and without it the joint is aligned by guesswork.
Tack the joint in two places opposite each other, check the run, then add two more. The check is not only for straightness: sight along the outside of the bend and confirm the curve is still continuous, with no flat spot at the joint and no kink where the arcs meet.
Welding pulls a joint towards the inside of the bend, so expect to correct for it. A joint tacked slightly open on the inside will close as it cools; one tacked tight will pull the bend sharper than it was, and the tip will end up where nobody planned.
Before the final seam, hang the section and look at where it sits. A bend that has been cut and rejoined is the part of the system most likely to hang a little differently, and the difference shows up as a tip off centre or a clearance that has closed.
Adjust at the joint while it is still tacked rather than at the hangers afterwards. On a run built as part of a stainless steel exhaust system, geometry is the point; where a replacement length is needed, a section from a known exhaust pipe range gives a bend with a consistent radius to work back to.
