What is meant by "the wrench simply turns either way"?. Is the head of the screw stripped out? Are you using the correct bit, torx vs allen?
If so, and you plan on tossing the mount, and you own a dremel tool (a hack saw will also work), you can use a cutoff wheel to slot the head of the screw (of course, you'll slot the mount too) and use a common screwdriver to remove.
Sometimes you can use a Torx bit in an allen head screw that is stripped with a few taps with a hammer to set it into the stripped head to start.
A judicious application of heat and liquid wrench can also be your friend in getting a stuck fastener released. Especially if locktite was used on the threads.
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