Firing a cw380 without the slide stop

Sounds like a dreadful idea.

with the slidestop out, cant you simply finish fieldstripping and then use a dowel from the muzzle end of the barrel to tap the round out??

I would not recomend trying to shoot it like that, the likely result could be damage from excessive rearward travel of the slide. I would find someone comfortable and confident to disassemble it. If the pin came out it sounds like the gun isnt in battery so i doubt it would fire anyway. Ive had kahr pistols before, theyre always finicky at best in my hand but theres a lot of love out there for them. I had a 45 kahr that after 200 or so rounds the slide would lift up 1/4" when the trigger was pulled - it was very unreliable. Be careful and please dont try to shoot a gun thats missing parts.
Maybe you can remove the backplate and pull the striker out, that should free the slide.

Please call Kahr and demand they solve the problem. DO NOT shoot the pistol without the slide stop.

You might use a padded vise. The rear extractor pin is sprung into the slide cover plate and is accessed via a small cutout. A small punch can press it down while you slide the plate free just enough to keep the rear extractor pin depressed. From there you would compress the striker spring and move the striker spring guide rod forward so it clears the plate (using a tool). At that point you can slide the plate off but obviously everything in there is under spring tension so don't lose an eye.

I have never done this with a chambered pistol, obviously this is not exactly a safe situation.

If you pull the trigger ( in a safe direction of course) the slide may just come off, i really dont think it would fire out of battery . Or maybe you can get at the striker tab through the magazine well ? If it were me i would pull the trigger, hold it to the rear and attempt to pull the slide back with some force if youre comfortable doing that. If not you should see a gunsmith (call first to explain the situation) , i doubt kahr wants you to send a gun with a chambered round in the mail but theyll tell you whats best. In any case keep that muzzle clear of anything you value and be safe.

Does the extractor have hold of the cartridge?

What ammo are you using? Just curious. I just had some remington JHP .380s from wally mart jam in the chamber of my new LCP. Heck of a time getting the slide back/round out.
New/better ammo- no apparent problems.
So again, just curious what ammo you have in there.

What caused it to jam?

Glad you got it cleared w/ no damage or injury!

glad you got it resolved.

I am not an operator nor do I really want to tell you what to do,..but, what happens and the forces applied when firing are different from simply hand cycling live rounds. it's much better to take the pistol apart and check several things with the ammo if you want to do that, like dropping a round in the chamber of a disassembled barrel/pistol, loading a mag and pushing the rounds back out by hand, loading mag and inserting in frame, etc.. on top of that, by hand cycling live rounds your increasing the odds of bullet set-back, it's something that can happen with HD or carry pistols that are loaded but then you want to practice so you unload it, use a snap cap and then chamber the same round over and over again. a good case for having multiples of the same primary pistol.

inspecting ammo is certainly a good idea, don't get me wrong, but it can be done several ways.