They usually aren't assuming you have SOMETHING to deal with them. Novice militia are not usually enough. They are big humanoids which means they have more "natural" armor (thicker skin etc.) which mean low tier weapons like copper or low skill levels may make it hard to hurt them. Also, they wrestle and punch (kick, misc. object user, gore etc.) by default which may mean full metal suits of armor won't be too useful. Don't bother with melee unless you have at least several skill levels in fighter and more than 1 soldier at a time.
Any kind of crossbow will be adequate to kill them (bone/ wood bolts, low quality bow). However, they will be totally useless if the minotaur can close with the xbowdwarf unless you get a lucky shot that incapacitates him somehow (somewhat unlikely if your militia has low skill.)
Cage traps are extremely effective, cheap, and reliable. Assuming you have the time to make mechanisms, cages, and build them.
you could try building a door and forbidding passage to buy yourself time. However, they are building destroyers so the time it buys you is related to the quality of the door, and may not be worth the effort.
Better solution would be to build a solid wall to block him out. (b>C>w I believe) block walls are erected in about 1/3 as much time as stone. Nothing can destroy constructed walls except fun things like cave-ins or idlers (children/ nobles usually) with the proper orders. you could then build traps at your leisure and let him in when you're prepared. Your corpses will eventually rot outside and cause ghosts and unhappy thoughts. So hurry unless that isn't a problem.
You could build Fortifications to block his movement but allow Line-of-sight (and therefore allow xbows to shoot him)
You could draft every dwarf and zerg rush him. which would be good for a laugh. If you don't deal with him, he will still be there if you reclaim. But you could bring soldiers and weapons on embark...
As far as the pathing and FPS drop: if dwarfs are forbidden to go outside somehow (like with burrows) you may get a lot of cancellation spam. the jobs being queued up and cancelled hundreds of times per second will cause a drop in FPS. Or dwarfs get a job, (pickup wounded soldier) see the minotaur and get scared, run back inside, forget the minotaur, get job (pickup wounded soldier) run back out... It's unlikely to be the clutter.
As for the minotaur: sometimes invaders forget what they are doing. Consider yourself lucky to have a few minutes of time to react. soldiers should ignore burrows and forbidden pathing so if you draft some peasants they should obey any move/ kill orders.