Help with thinly slicing garlic

For the general case of cutting vegetables, I will always recommend a mandoline. Cutting with a mandoline vs. knife is like drawing a straight line with ruler vs. without - even though very experienced people can get good results both ways, using the mandoline is always quicker and more precise. And for anybody whose fine motoric skills are compromised, the mandoline adds even more value than for the average person.

But the main disadvantage of the mandoline is that it doesn't work so well with the "butt" of the vegetable. With a normal-sized mandoline, I usually start using the cap when the food is worn down enough to pass about 4-5 cm above the blade, and because the cap is fiddly when the food is too thin, I leave the last 1 cm unsliced. There is no problem with making paper-thin slices of something large like an apple; but I would be wary of slicing something smaller than a garden radish on the normal mandoline, and wouldn't attempt a single garlic clove.

The small garlic mandoline looks like it is designed to solve this problem, as a video of it shows that you can push it down inside a holding "cell" instead of having to rely on a nail to hold it in place as with traditional mandoline caps. But it might still lead to large butts (which you can of course process as per Kate Gregory's answer).

Another thing important about a mandoline is that it should stand on a surface by its own. Mine has a rotating frame in the back which lets it stand stable on the counter, like a tablet holder. I only have to move the vegetable while the mandoline remains stable. Some have holes in the bottom edge so they can be put on a bowl rim. I can't see such a mechanism in the one you linked. If it requires the use of both hands (hold it stable with one hand while slicing with the other), its usability will be diminished a lot, especially when you have trouble with muscle coordination. You should try to find a model which can stand stable on its own. The person in the video does not use such a mechanism, maybe you should write to the manufacturer and ask if it exists.

The first half of the clove is easiest to slice, since you have something to hold on to. Since you will use up food-processed and frozen garlic, I suggest you use two "first halves" every time you want a clove of finely sliced garlic, then process the two second halves for later use. (Don't want to use the food processor for such a tiny job? Try a garlic chopper like this. They look ridiculous but work (I was given one) and clean in the dishwasher.)

If you want to slice the second half, try rotating it so the cut surface is down on the board. This makes everything more stable. Take a break to let your hands relax if you need to.

The most safe way would be to choose big cloves, and only slice about half of the clove, using the other half for something else, so plenty of garlic remains that allows a proper claw grip (using a knuckle to guide the blade on while holding the garlic down with a finger that is several mm away from the blade). Slicing the clove in half (in the other direction) beforehand helps making a stable surface for the garlic to stand on. Also, use a thin (thin edged so you cut with very little force, and thin spined so the spine doesn't obstruct your view down the blade - might I recommend a Kom Kom/Kiwi for a cheap option?) knife.