I've seen overloaded drivers that were so overheated that the magnet fell off - some not so rugged epoxy adhesive was used - along with wishful ratings on the labelling.
So, heat. I'm not sure how alnico holds it's bias under moderate limits. The magnets are formed from raw material by application of an external field. A very high field for a short time.
I assume it can be degraded by mechanical shock, heat or other abuse.
The magnets look like ferrite, so temps of upto 180C should be safe, and that's more than enough to soften any epoxy they may have used for assembly to the yoke. Be sure to use eye protection when fussing with magnets like that.
I'll defer to Phil on exact construction details but most likely the magnet was installed by sliding it on from the side, so it should go back off that way. Take two short 2x4" boards (or similar), lay on one top of the other with wide sides touching and one pair of ends aligned, and then put in one long screw near those ends. Don't tighten it all the way up so the boards can pivot, and you now have kind of giant pair of scissors. "Open" the scissors and lay the speaker in so that the magnet rests on the bottom board and the top board contacts the speaker frame, and close the scissors. Depending on the magnet strength this can get fancier, for example cut a round hole in one board and insert the magnet for more control, or cut a small notch in each board so the speaker won't try to slip away, etc. You might be able to get away with some heat if there is glue to soften, but my expectation is that any hammering and you might as well put it back in the dumpster now and save the work :-). Someone asked how a magnet can harm the skin - that comes with the rest of the tissue damage if you let part of you get pinched between the magnet and a piece of iron or steel. My favorite NdFeB magnet supplier is kjmagnetics.com. They have lots of fun videos on youtube where they let magnets fly into other magnets and steel plates, with various things in the way.
** All magnets have a " Curie " temperature - at which all magnetisation is lost. Usually is is not self recovering. However, for speaker magnets that temp is beyond the range of a domestic oven.
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When disassembling speaker magnets from their iron parts, repairers use a de-magnetising electromagnet. Same one used for magnetising during manufacture but operated in reverse.
Such electromagnets are brute force devices, big and heavy employing rectified mains current for brief periods.
If the OP needs a strong magnetic field - he should leave the damn thing fully assembled as I already posted.
Fuck dopey OPs who will not say what they actually want .
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