You should only cut the top of the top most flue pipe. Typically the drum installed in the suspension plate is cut at the roof line. The starter flue (with damper) is only cut at the top if it is the only flue pipe, if at all.
If there is an addition flue pipe above the starter flue, it can be cut at the top only.
This video will give an example of to cut the flue pipe or suspension drum with a angle grinder.