How would they be completely destroyed? The only way I can think of is by encirclement, and to accomplish this, the BEF would need to be monumentally stupid.
There is the possibility that the BEF gets disintegrated on the retreat, however. It is a scant one. The BEF retreated in good order and before the French Fifth Army was in real danger. Perhaps get the French Fifth Army to retreat in disorder and end up crossing the path of the BEF and cause utter chaos, and combine this with the BEF deciding to hold at Mons for another few days and foolishly take a lot of casualties. On the Great Retreat, units were lost whole sale and equipment abandoned, but none in any kind of levels that threaten the BEF's ability to fight in France.
A chaotic disorderly retreat could see the elements of the two corps engaged at Mons to be picked apart and crack under the stress of a retreat in which the French clog their escape routes. This was more possible than I think people like to admit.
However, as for being destroyed on the field at Mons, I don't see it happening. WW1 armies lacked the ability to do that kind of thing, and encirclement seems almost impossible in my opinion. I guess if they chose not to retreat when they did OTL, its possible, but I doubt it. Or maybe if they fall back on the Belgian coast rather than on the Marne because of a screwup in orders, they could be isolated and eventually destroyed or forced to pull a Dunkirk 26 years early.