Pictorial explanation - or at least a try:
1. You need two of those (you can manage with one, but two is easier - you need something to FIRMLY hold the bracelet.):
2. Remove bracelet from watch. Remove clasp from bracelet.
3. (In this picture I have obviously not done step 2 - it is only to try to explain what I earlier wrote... and you need two wire cutters - or pliers). Put the cutting edges where the middle part of the link meets the outer part:
4. Apply pressure (heavy!):
Obviously this is done after the clasp has been removed, so the permanent link being removed is free. Here is a close-up. Imagine the links below the cutter not being there.
As you apply pressure the gap between the middle and outer part will widen, and as the gaps grow wider the grip of the (hidden) pin will be lost. Do not try to bend the outer part to get it off. Do not put pressure on the outer part either, since that will increase the force keeping the pin in place.
Here is again the (lended) picture of the separated link.
I'll try to remember to document how I do this the next time I do it. In addition: Use tape to cover all parts. It is too easy to damage a link, that is supposed to be left. I did it the first time, but only on the inside (not visible).
PM me if this is completely impossible to understand!
(My AD taught me how to do it.)
Best,
A