A replacement one will normally be flared at the end to allow it to slide onto where the old one has been cut off (should be a sliding fit, not really loose), then you clamp where the two overlap with an exhaust clamp (u bolt clamp is simplest) and maybe use some exhaust sealing paste.

Are you saying you've cut too much off the old system?
If that's the case the mounts will probably still fit but if the pipe exits through the bumper it will look wrong if it's too short so you might have to get a length of pipe welded on to match it back up.