When you get the bushhog or other cutter it should come with a PTO shaft to attach to the tractor PTO output shaft. You won't be switching PTO shafts between driven implements.
I've only had to cut shafts when replacing on used equipment, but every implement-tractor combination is different.
Hook up the implement to the 3-point (leave the PTO shaft dangling loose, not connected to the tractor) and carefully lift the implement using the tractor 3-point hydraulics. Don't bind the loose shaft. Observe its position, height above ground.
Now lower the implement to the ground, shut everything off, and hook up PTO shaft to tractor. Make sure the snap-collar properly engages.
Lift again, observing how implement acts. Lift slowly on first gyration. As the PTO shaft telescopes it may --if too long-- bottom out one piece of the shaft inside the other. Be gentle and watch carefully.
If implement returns to 'unconnected' position when it is connected and you observe no binding or clunking bottoming-out of the shaft, you're good.
If you note interference or the implement or the implement won't lift to original position, you need to shorten the shaft.
You'll have to figure out how to measure the difference and if the excess needs to come off the external tube or internal insert or even both. You'll also need to figure out how to get the blasted PTO plastic safety guard off the shaft(s).
Depending on your skill and tools you can cut shaft(s) with torch or chop saw or recip saw or hacksaw if patient. Be sure to reattach safety shroud.
Grease all U-joints, keep them greased, and check gearbox and keep filled per manual. I oil my PTO shafts by pouring oil on them as I work them up and down and wiring an old rag at the joint as a wiper.
If bushhog, expect to sharpen blades with hand grinder after removing and be aware that blades do bend and can break. I've run across some bushhogs that no longer have top deck ports to access the nuts of the blade bolts. Expect to cut a hole in deck to prevent having to remove the stump-jumper (often after some use it can't easily be removed).
Please post back your experiences so we may all learn.